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日本原子力研究開発機構機関リポジトリ Japan Atomic Energy Agency Institutional Repository

Title Dielectron production in Au + Au collisions at √𝑠𝑠_𝑁𝑁𝑁𝑁=200 GeV

Author(s) Adare A., Hasegawa Shoichi, Imai Kenichi, Nagamiya Shoji, Sako Hiroyuki, Sato Susumu, Tanida Kiyoshi, PHENIX Collaboration, 440 of others

Citation Physical Review C, 93(1), p.014904_1-014904_34

Text Version Publisher's Version

URL https://jopss.jaea.go.jp/search/servlet/search?5054950

DOI https://doi.org/10.1103/PhysRevC.93.014904

Right © 2016 The American Physical Society

PHYSICAL REVIEW C 93, 014904 (2016)

Dielectron production in Au + Au collisions at√

sN N = 200 GeV

A. Adare,13 C. Aidala,40,45 N. N. Ajitanand,64 Y. Akiba,58,59 R. Akimoto,12 J. Alexander,64 M. Alfred,24 H. Al-Ta’ani,52

A. Angerami,14 K. Aoki,33,58 N. Apadula,29,65 Y. Aramaki,12,58 H. Asano,36,58 E. C. Aschenauer,7 E. T. Atomssa,65

R. Averbeck,65 T. C. Awes,54 B. Azmoun,7 V. Babintsev,25 M. Bai,6 N. S. Bandara,44 B. Bannier,65 K. N. Barish,8

B. Bassalleck,51 S. Bathe,5,59 V. Baublis,57 S. Baumgart,58 A. Bazilevsky,7 M. Beaumier,8 S. Beckman,13 R. Belmont,13,45,69

A. Berdnikov,61 Y. Berdnikov,61 D. S. Blau,35 J. S. Bok,51,52,72 K. Boyle,59 M. L. Brooks,40 J. Bryslawskyj,5 H. Buesching,7

V. Bumazhnov,25 S. Butsyk,51 S. Campbell,14,29,65 P. Castera,65 C.-H. Chen,59,65 C. Y. Chi,14 M. Chiu,7 I. J. Choi,26

J. B. Choi,10 S. Choi,63 R. K. Choudhury,4 P. Christiansen,42 T. Chujo,68 O. Chvala,8 V. Cianciolo,54 Z. Citron,65,70

B. A. Cole,14 M. Connors,65 M. Csanad,18 T. Csorgo,71 S. Dairaku,36,58 T. W. Danley,53 A. Datta,44,51 M. S. Daugherity,1

G. David,7 K. DeBlasio,51 K. Dehmelt,65 A. Denisov,25 A. Deshpande,59,65 E. J. Desmond,7 K. V. Dharmawardane,52

O. Dietzsch,62 L. Ding,29 A. Dion,29,65 P. B. Diss,43 J. H. Do,72 M. Donadelli,62 L. D’Orazio,43 O. Drapier,37 A. Drees,65

K. A. Drees,6 J. M. Durham,40,65 A. Durum,25 S. Edwards,6 Y. V. Efremenko,54 T. Engelmore,14 A. Enokizono,54,58,60

S. Esumi,68 K. O. Eyser,7,8 B. Fadem,46 N. Feege,65 D. E. Fields,51 M. Finger,9 M. Finger, Jr.,9 F. Fleuret,37 S. L. Fokin,35

J. E. Frantz,53 A. Franz,7 A. D. Frawley,20 Y. Fukao,58 T. Fusayasu,49 K. Gainey,1 C. Gal,65 P. Gallus,15 P. Garg,3

A. Garishvili,66 I. Garishvili,39 H. Ge,65 F. Giordano,26 A. Glenn,39 X. Gong,64 M. Gonin,37 Y. Goto,58,59 R. Granier deCassagnac,37 N. Grau,2 S. V. Greene,69 M. Grosse Perdekamp,26 T. Gunji,12 L. Guo,40 H.-A. Gustafsson,42,* T. Hachiya,58

J. S. Haggerty,7 K. I. Hahn,19 H. Hamagaki,12 H. F. Hamilton,1 S. Y. Han,19 J. Hanks,14,65 S. Hasegawa,30 T. O. S. Haseler,21

K. Hashimoto,58,60 E. Haslum,42 R. Hayano,12 X. He,21 T. K. Hemmick,65 T. Hester,8 J. C. Hill,29 R. S. Hollis,8 K. Homma,23

B. Hong,34 T. Horaguchi,68 Y. Hori,12 T. Hoshino,23 N. Hotvedt,29 J. Huang,7 S. Huang,69 T. Ichihara,58,59 H. Iinuma,33

Y. Ikeda,58,68 K. Imai,30 J. Imrek,17 M. Inaba,68 A. Iordanova,8 D. Isenhower,1 M. Issah,69 D. Ivanishchev,57 B. V. Jacak,65

M. Javani,21 M. Jezghani,21 J. Jia,7,64 X. Jiang,40 B. M. Johnson,7 K. S. Joo,47 D. Jouan,55 D. S. Jumper,26 J. Kamin,65

S. Kanda,12 S. Kaneti,65 B. H. Kang,22 J. H. Kang,72 J. S. Kang,22 J. Kapustinsky,40 K. Karatsu,36,58 M. Kasai,58,60

D. Kawall,44,59 A. V. Kazantsev,35 T. Kempel,29 J. A. Key,51 V. Khachatryan,65 A. Khanzadeev,57 K. M. Kijima,23 B. I. Kim,34

C. Kim,34 D. J. Kim,31 E.-J. Kim,10 G. W. Kim,19 H. J. Kim,72 K.-B. Kim,10 M. Kim,63 Y.-J. Kim,26 Y. K. Kim,22

B. Kimelman,46 E. Kinney,13 A. Kiss,18 E. Kistenev,7 R. Kitamura,12 J. Klatsky,20 D. Kleinjan,8 P. Kline,65 T. Koblesky,13

Y. Komatsu,12,33 B. Komkov,57 J. Koster,26 D. Kotchetkov,53 D. Kotov,57,61 A. Kral,15 F. Krizek,31 G. J. Kunde,40 K. Kurita,58,60

M. Kurosawa,58,59 Y. Kwon,72 G. S. Kyle,52 R. Lacey,64 Y. S. Lai,14 J. G. Lajoie,29 A. Lebedev,29 B. Lee,22 D. M. Lee,40

J. Lee,19 K. B. Lee,34 K. S. Lee,34 S Lee,72 S. H. Lee,65 S. R. Lee,10 M. J. Leitch,40 M. A. L. Leite,62 M. Leitgab,26 B. Lewis,65

X. Li,11 S. H. Lim,72 L. A. Linden Levy,13 M. X. Liu,40 B. Love,69 D. Lynch,7 C. F. Maguire,69 Y. I. Makdisi,6 M. Makek,70,73

A. Manion,65 V. I. Manko,35 E. Mannel,7,14 S. Masumoto,12,33 M. McCumber,13,40 P. L. McGaughey,40 D. McGlinchey,13,20

C. McKinney,26 A. Meles,52 M. Mendoza,8 B. Meredith,26 Y. Miake,68 T. Mibe,33 A. C. Mignerey,43 A. Milov,70 D. K. Mishra,4

J. T. Mitchell,7 Y. Miyachi,58,67 S. Miyasaka,58,67 S. Mizuno,58,68 A. K. Mohanty,4 S. Mohapatra,64 P. Montuenga,26

H. J. Moon,47 T. Moon,72 D. P. Morrison,7,† S. Motschwiller,46 T. V. Moukhanova,35 T. Murakami,36,58 J. Murata,58,60

A. Mwai,64 T. Nagae,36 S. Nagamiya,33,58 K. Nagashima,23 J. L. Nagle,13,‡ M. I. Nagy,18,71 I. Nakagawa,58,59 H. Nakagomi,58,68

Y. Nakamiya,23 K. R. Nakamura,36,58 T. Nakamura,58 K. Nakano,58,67 C. Nattrass,66 A. Nederlof,46 P. K. Netrakanti,4

M. Nihashi,23,58 T. Niida,68 S. Nishimura,12 R. Nouicer,7,59 T. Novak,32,71 N. Novitzky,31,65 A. S. Nyanin,35 E. O’Brien,7

C. A. Ogilvie,29 K. Okada,59 J. D. Orjuela Koop,13 J. D. Osborn,45 A. Oskarsson,42 M. Ouchida,23,58 K. Ozawa,12,33 R. Pak,7

V. Pantuev,27 V. Papavassiliou,52 B. H. Park,22 I. H. Park,19 J. S. Park,63 S. Park,63 S. K. Park,34 S. F. Pate,52 L. Patel,21

M. Patel,29 H. Pei,29 J.-C. Peng,26 H. Pereira,16 D. V. Perepelitsa,7,14 G. D. N. Perera,52 D. Yu. Peressounko,35 J. Perry,29

R. Petti,7,65 C. Pinkenburg,7 R. Pinson,1 R. P. Pisani,7 M. Proissl,65 M. L. Purschke,7 H. Qu,1 J. Rak,31 B. J. Ramson,45

I. Ravinovich,70 K. F. Read,54,66 D. Reynolds,64 V. Riabov,50,57 Y. Riabov,57,61 E. Richardson,43 T. Rinn,29 D. Roach,69

G. Roche,41,* S. D. Rolnick,8 M. Rosati,29 Z. Rowan,5 J. G. Rubin,45 B. Sahlmueller,65 N. Saito,33 T. Sakaguchi,7 H. Sako,30

V. Samsonov,50,57 M. Sano,68 M. Sarsour,21 S. Sato,30 S. Sawada,33 B. Schaefer,69 B. K. Schmoll,66 K. Sedgwick,8

R. Seidl,58,59 A. Sen,21,66 R. Seto,8 P. Sett,4 A. Sexton,43 D. Sharma,65,70 I. Shein,25 T.-A. Shibata,58,67 K. Shigaki,23

M. Shimomura,29,48,68 K. Shoji,36,58 P. Shukla,4 A. Sickles,7,26 C. L. Silva,29,40 D. Silvermyr,42,54 K. S. Sim,34 B. K. Singh,3

C. P. Singh,3 V. Singh,3 M. Slunecka,9 M. Snowball,40 R. A. Soltz,39 W. E. Sondheim,40 S. P. Sorensen,66 I. V. Sourikova,7

P. W. Stankus,54 E. Stenlund,42 M. Stepanov,44,* A. Ster,71 S. P. Stoll,7 T. Sugitate,23 A. Sukhanov,7 T. Sumita,58 J. Sun,65

J. Sziklai,71 E. M. Takagui,62 A. Takahara,12 A. Taketani,58,59 Y. Tanaka,49 S. Taneja,65 K. Tanida,59,63 M. J. Tannenbaum,7

S. Tarafdar,3,70 A. Taranenko,50,64 E. Tennant,52 H. Themann,65 R. Tieulent,21 A. Timilsina,29 T. Todoroki,58,68 L. Tomasek,28

M. Tomasek,15,28 H. Torii,23 C. L. Towell,1 R. Towell,1 R. S. Towell,1 I. Tserruya,70 Y. Tsuchimoto,12 T. Tsuji,12 C. Vale,7

H. W. van Hecke,40 M. Vargyas,18 E. Vazquez-Zambrano,14 A. Veicht,14 J. Velkovska,69 R. Vertesi,71 M. Virius,15 A. Vossen,26

V. Vrba,15,28 E. Vznuzdaev,57 X. R. Wang,52,59 D. Watanabe,23 K. Watanabe,68 Y. Watanabe,58,59 Y. S. Watanabe,12,33

F. Wei,29,52 R. Wei,64 A. S. White,45 S. N. White,7 D. Winter,14 S. Wolin,26 C. L. Woody,7 M. Wysocki,13,54 B. Xia,53 L. Xue,21

S. Yalcin,65 Y. L. Yamaguchi,12,58,65 R. Yang,26 A. Yanovich,25 J. Ying,21 S. Yokkaichi,58,59 J. H. Yoo,34 I. Yoon,63 Z. You,40

I. Younus,38,51 H. Yu,56 I. E. Yushmanov,35 W. A. Zajc,14 A. Zelenski,6 S. Zhou,11 and L. Zou8

(PHENIX Collaboration)1Abilene Christian University, Abilene, Texas 79699, USA

2469-9985/2016/93(1)/014904(34) 014904-1 ©2016 American Physical Society

A. ADARE et al. PHYSICAL REVIEW C 93, 014904 (2016)

2Department of Physics, Augustana University, Sioux Falls, South Dakota 57197, USA3Department of Physics, Banaras Hindu University, Varanasi 221005, India

4Bhabha Atomic Research Centre, Bombay 400 085, India5Baruch College, City University of New York, New York, New York 10010, USA

6Collider-Accelerator Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA7Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA

8University of California-Riverside, Riverside, California 92521, USA9Charles University, Ovocny trh 5, Praha 1, 116 36 Prague, Czech Republic

10Chonbuk National University, Jeonju 561-756, Korea11Science and Technology on Nuclear Data Laboratory, China Institute of Atomic Energy, Beijing 102413, People’s Republic of China

12Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan13University of Colorado, Boulder, Colorado 80309, USA

14Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA15Czech Technical University, Zikova 4, 166 36 Prague 6, Czech Republic

16Dapnia, CEA Saclay, F-91191 Gif-sur-Yvette, France17Debrecen University, H-4010 Debrecen, Egyetem ter 1, Hungary

18ELTE, Eotvos Lorand University, H-1117 Budapest, Pazmany P. s. 1/A, Hungary19Ewha Womans University, Seoul 120-750, Korea

20Florida State University, Tallahassee, Florida 32306, USA21Georgia State University, Atlanta, Georgia 30303, USA

22Hanyang University, Seoul 133-792, Korea23Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan

24Department of Physics and Astronomy, Howard University, Washington, DC 20059, USA25IHEP Protvino, State Research Center of Russian Federation, Institute for High Energy Physics, Protvino 142281, Russia

26University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA27Institute for Nuclear Research of the Russian Academy of Sciences, prospekt 60-letiya Oktyabrya 7a, Moscow 117312, Russia

28Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic29Iowa State University, Ames, Iowa 50011, USA

30Advanced Science Research Center, Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai-mura, Naka-gun,Ibaraki-ken 319-1195, Japan

31Helsinki Institute of Physics and University of Jyvaskyla, P.O. Box 35, FI-40014 Jyvaskyla, Finland32Karoly Roberts University College, H-3200 Gyongyos, Matraiut 36, Hungary

33KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan34Korea University, Seoul 136-701, Korea

35National Research Center “Kurchatov Institute,” Moscow, 123098, Russia36Kyoto University, Kyoto 606-8502, Japan

37Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay, F-91128 Palaiseau, France38Physics Department, Lahore University of Management Sciences, Lahore 54792, Pakistan

39Lawrence Livermore National Laboratory, Livermore, California 94550, USA40Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

41LPC, Universite Blaise Pascal, CNRS-IN2P3, Clermont-Fd, 63177 Aubiere Cedex, France42Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden

43University of Maryland, College Park, Maryland 20742, USA44Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003-9337, USA

45Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA46Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA

47Myongji University, Yongin, Kyonggido 449-728, Korea48Nara Women’s University, Kita-uoya Nishi-machi, Nara 630-8506, Japan

49Nagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki 851-0193, Japan50National Research Nuclear University, MEPhI, Moscow Engineering Physics Institute, Moscow 115409, Russia

51University of New Mexico, Albuquerque, New Mexico 87131, USA52New Mexico State University, Las Cruces, New Mexico 88003, USA

53Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA54Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

55IPN-Orsay, Universite Paris-Sud, CNRS/IN2P3, Universite Paris-Saclay, BP1, F-91406 Orsay, France56Peking University, Beijing 100871, People’s Republic of China

57PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad Region 188300, Russia58RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan

59RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA

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DIELECTRON PRODUCTION IN Au + Au COLLISIONS . . . PHYSICAL REVIEW C 93, 014904 (2016)

60Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan61Saint Petersburg State Polytechnic University, St. Petersburg 195251, Russia

62Universidade de Sao Paulo, Instituto de Fısica, Caixa Postal 66318, Sao Paulo CEP05315-970, Brazil63Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea

64Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA65Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA

66University of Tennessee, Knoxville, Tennessee 37996, USA67Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan

68Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Ibaraki 305, Japan69Vanderbilt University, Nashville, Tennessee 37235, USA

70Weizmann Institute, Rehovot 76100, Israel71Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Hungarian Academy of Sciences (Wigner RCP, RMKI)

H-1525 Budapest 114, PO Box 49, Budapest, Hungary72Yonsei University, IPAP, Seoul 120-749, Korea

73University of Zagreb, Faculty of Science, Department of Physics, Bijenicka 32, HR-10002 Zagreb, Croatia(Received 5 October 2015; published 11 January 2016)

We present measurements of e+e− production at midrapidity in Au + Au collisions at√

sNN

= 200 GeV. Theinvariant yield is studied within the PHENIX detector acceptance over a wide range of mass (mee < 5 GeV/c2)and pair transverse momentum (pT < 5 GeV/c) for minimum bias and for five centrality classes. The e+e− yieldis compared to the expectations from known sources. In the low-mass region (mee = 0.30–0.76 GeV/c2) thereis an enhancement that increases with centrality and is distributed over the entire pair pT range measured. Itis significantly smaller than previously reported by the PHENIX experiment and amounts to 2.3 ± 0.4(stat) ±0.4(syst) ± 0.2(model) or to 1.7 ± 0.3(stat) ± 0.3(syst) ± 0.2(model) for minimum bias collisions when theopen heavy-flavor contribution is calculated with PYTHIA or MC@NLO, respectively. The inclusive mass andpT distributions, as well as the centrality dependence, are well reproduced by model calculations where theenhancement mainly originates from the melting of the ρ meson resonance as the system approaches chiralsymmetry restoration. In the intermediate-mass region (mee = 1.2–2.8 GeV/c2), the data hint at a significantcontribution in addition to the yield from the semileptonic decays of heavy-flavor mesons.

DOI: 10.1103/PhysRevC.93.014904

I. INTRODUCTION

Dileptons are important diagnostic tools of the quark-gluonplasma (QGP) formed in ultrarelativistic heavy-ion collisions[1]. They are unique observables for their sensitivity tothe chiral symmetry restoration phase transition expectedto take place together with, or at similar conditions to, thedeconfinement phase transition [2,3]. When chiral symmetryis restored, the chiral doublets, such as the ρ and the a1 mesons,become degenerate in mass. Because the a1 meson is verydifficult to observe experimentally, the ρ meson is the mainobservable in this context. Owing to its very short lifetime(τ ∼ 1.3 fm/c), the ρ meson quickly decays after its formationand is therefore a sensitive probe of the medium where it isformed. The ρ meson is mostly produced close to the phaseboundary, and possible modifications of its spectral functionin the high-temperature and -density conditions prevailingthere are thus imprinted in its decay products. The decay intodileptons, as opposed to hadrons, is of particular interest asthey escape unaffected by the interaction region, thus carryingthis information to the detectors.

*Deceased.†PHENIX cospokesperson; morrison@bnl.gov‡PHENIX cospokesperson; jamie.nagle@colorado.edu

Dileptons are sensitive to the thermal radiation emittedby the system, both the partonic thermal radiation (quarkannihilation into virtual photons, qq → γ ∗ → l+l−) emittedin the early stage of the collisions and the thermal radiationemitted later in the collision by the hadronic system. The mainchannel of the latter is pion annihilation, mediated throughvector meson dominance by the ρ meson (π+π− → ρ →γ ∗ → l+l−). Dileptons are produced by a variety of sourcesall along the entire history of the collision and it is necessaryto know precisely all these sources to single out the interestingsignals characteristic of the QGP related to chiral symmetryrestoration or thermal radiation [4].

The CERES experiment pioneered the study of dielectronsat the Super Proton Synchrotron (SPS). A strong enhancementof low-mass electron pairs (mee < 1 GeV/c2) with respect tothe cocktail of expected hadronic sources was found in allnuclear systems studied, in S + Au collisions at 200 A GeV[5], in Pb + Au collisions at 158 A GeV [6,7], and in Pb + Aucollisions at 40 A GeV [8]. The enhancement was confirmedand further studied by the high statistics NA60 experiment thatmeasured dimuons in In + In collisions at 160 A GeV [9–12].In both experiments, the low-mass dilepton enhancement isexplained by in-medium modification of the ρ meson spectralfunction [13–18]. The data rule out the conjectured droppingmass of the ρ meson as the system approaches chiral symmetryrestoration [19–21]. Instead, the data are well reproduced by ascenario in which the ρ meson copiously produced by π+π−

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A. ADARE et al. PHYSICAL REVIEW C 93, 014904 (2016)

annihilation is broadened by the scattering off baryons in thedense hadronic medium. The low-mass dilepton excess is thusidentified as the thermal radiation signal from the hadron-gasphase with a modified ρ meson spectral function. A recentpaper shows that in-medium modifications of vector and axialvector spectral functions lead to degeneracy of the ρ and a1

meson masses, providing a direct link between the broadeningof the ρ meson spectral function and the restoration of chiralsymmetry [22].

NA60 found also an excess at higher masses (ml+l− = 1–3GeV/c2). Using precise vertex information, this excess wasassociated with a prompt source originating at the vertex, asopposed to semileptonic decays of D mesons that originateat displaced vertices. The excess can be explained as thermalradiation from the QGP [9–12,15], but other interpretationsbased on hadronic models, similar to those that explain the lowmass excess [13,14], or on hadronic rates constrained by chiralsymmetry considerations [16], can also reproduce the data.

At the Relativistic Heavy Ion Collider (RHIC), the PHENIXexperiment reported a strong enhancement of low-mass pairsin Au + Au collisions at

√s

NN= 200 GeV [23]. In the 0%–

10% most central collisions, where the excess is concentrated,the enhancement factor, defined as the ratio of the measuredyield over the cocktail yield reaches an average value of 7.6 ±0.5(stat) ± 1.3(syst) ± 1.5(cocktail) in the mass range mee =0.15–0.75 GeV/c2. All models that successfully reproduce theSPS results fail to explain the PHENIX data [23,24].

The PHENIX result [23] was characterized by a consid-erable hadron contamination of the electron sample and by asmall signal-to-background (S/B) ratio. In an effort to improveupon this measurement, a hadron-blind detector (HBD) wasdeveloped and installed in the PHENIX experiment [25–27].The HBD provides additional electron identification andadditional hadron rejection and improves the signal sensitivity.

In this paper we present dielectron results obtained withthe HBD in 2010 for Au + Au collisions at

√s

NN= 200 GeV.

The paper is organized as follows. Section II describes thePHENIX detector with special emphasis on the HBD. InSec. III we give a detailed account of the various steps ofthe data analysis including electron identification, pair cuts,and background subtraction, which is the crucial step in thisanalysis. The raw mass spectra, efficiency corrections andsystematic uncertainties of the data are also discussed in thissection. Section IV describes the procedures used to calculatethe expected dielectron yield from the known hadronic sources.The results, including invariant mass spectra, pT distributions,and centrality dependence, are presented in Sec. V. In thesame section, the results are discussed with respect to previ-ously published results and compared to available theoreticalcalculations. A summary is given in Sec. VI.

II. PHENIX DETECTOR

Figure 1 shows a schematic beam view of the PHENIXcentral-arm detector, as used during 2010 data taking. A de-tailed description of the detector, except the HBD, can be foundin Ref. [28]. In this section, we give only a brief descriptionof the PHENIX subsystems relevant for the present analysis:global detectors, central magnet, central-arm detectors, includ-

West Beam View

PHENIX Detector2010

East

HBD

PbSc PbSc

PbSc PbSc

PbSc PbGl

PbSc PbGl

TOF-E

PC1 PC1

PC3PC2

CentralMagnet TEC

PC3

BB

RICH RICH

DC DC

Aerogel

TOF-W 7.9 m = 26 ft

FIG. 1. Beam view (at z = 0) of the PHENIX central armspectrometers during 2010 data taking.

ing drift chambers (DCs), pad chambers (PCs), ring-imagingCerenkov (RICH) detectors, time-of-flight (TOF) detectors,and electromagnetic calorimeters (EMCAL) and the HBD.

A. Global detectors

The measurement of the collision-vertex position, time,and centrality, as well as the minimum-bias (MB) trigger,is provided by two beam-beam counters (BBCs) [29]. EachBBC comprises 64 quartz Cerenkov counters, located at±144 cm along the beam axis from the center of PHENIX,with 2π azimuthal coverage over the pseudorapidity interval3.0 < |η| < 3.9. The collision-vertex position along the beamdirection z is determined from the difference of the average hittime of the photomultiplier tubes (PMTs) between the northand the south BBCs. The z-vertex resolution ranges from ∼0.5cm in central Au + Au collisions to ∼2 cm in p + p collisions.The MB trigger requires a coincidence between at least twohits in each of the BBC arrays, thus capturing 92% ± 3% ofthe total inelastic cross section [30].

B. Central magnet

The PHENIX central magnet comprises two pairs ofconcentric coils, an inner coil pair and an outer coil pair, thatcan be operated independently and create an axial magneticfield parallel to the beam axis [31]. The coils are usuallyoperated with current flowing in the same direction (the ++ or−− configuration) so that their magnetic fields add together.For the dilepton measurement with the HBD in the 2010 run,the coils were operated with equal currents flowing in oppositedirections. In this so-called +− configuration, the inner coilcounteracts the action of the outer coil so that their magneticfields cancel each other, creating an almost field-free region inthe inner space extending from the beam axis out to a radialdistance of ∼60 cm, where the inner coil is located (see Fig. 1of Ref. [27]). The field-free region preserves the opening angleof e+e− pairs and this is an essential prerequisite for theoperation of the HBD. The HBD exploits the fact that theopening angle of e+e− pairs originating from γ conversions

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DIELECTRON PRODUCTION IN Au + Au COLLISIONS . . . PHYSICAL REVIEW C 93, 014904 (2016)

or from π0 Dalitz decays is very small. When only one ofthe two tracks is reconstructed in the central arms, the HBDcan reject them by applying an opening angle cut or a doublesignal cut on the HBD hits (see Sec. II D). In this configuration,however, the total field integral is

∫B · dl = 0.43 Tm, about

40% of the value in the ++ configuration.

C. Central-arm detectors

PHENIX measurements at midrapidity are made with twocentral-arm spectrometers, as shown in Fig. 1. Each centralarm covers pseudorapidity |η| < 0.35 and azimuthal angle�φ = π/2.

Charged-particle tracks are reconstructed using hit infor-mation from the DC, the first layer of PC (PC1), and thecollision point along the z direction [32]. The DCs are locatedoutside the magnetic field in the radial distance 2.02–2.46 mfrom the beam axis. They provide an accurate measurement ofthe particle trajectory in the plane perpendicular to the beamaxis. The PC1s are multiwire proportional chambers locatedjust behind the DC at 2.47–2.52 m in radial distance from thebeam axis [33]. They provide a three-dimensional space pointthat is used to determine the track origin along the beam axis.The transverse momentum (pT ) of each particle is determinedfrom the bending of its trajectory in the azimuthal direction.The total momentum p is determined by combining pT withthe polar angle information of PC1 and the vertex positionz. The reconstructed tracks are projected onto the HBD (seenext section) and onto the central-arm detectors that provideelectron identification: RICH, EMCal, and TOF.

The RICH is the primary central-arm detector used forelectron identification in PHENIX [34] and is located in theradial region of 2.5–4.1 m, just behind PC1. The RICH usesCO2 as the gas radiator at atmospheric pressure, and has aCerenkov threshold of γ = 35. This corresponds to a momen-tum threshold of 18 MeV/c for electrons and 4.7 GeV/c forpions. Two spherical mirrors reflect the Cerenkov light andfocus it onto two arrays of 1280 PMTs, each located outsidethe acceptance on each side of the RICH entrance window.The average number of hit PMTs per electron track is ∼5,and the average number of photoelectrons detected is ∼10.Below the pion threshold, the pion rejection is ∼104 in p + por low-multiplicity collisions. However, in high-multiplicitycollisions, hadron tracks are misidentified as electrons whentheir trajectory is nearly parallel to that of a genuine electron.This effect limits the e/π separation to ∼10−3 in centralAu + Au collisions and requires special care as describedbelow.

The EMCal measures the energy deposited by electronsand their shower shape [35]. It comprises eight sectors eachcovering �φ ≈ π/8 in azimuth, where six sectors are madefrom lead-scintillator (PbSc) with an energy resolution 4.5% ⊕8.3%/

√E [GeV] and two are lead-glass (PbGl) with an energy

resolution 4.3% ⊕ 7.7%/√

E [GeV]. The radial distance fromthe beam axis is 5.10 m for PbSc and 5.50 m for PbGl (seeFig. 1). The matching of the measured energy to the trackmomentum is used to identify electrons. The latter are all rel-ativistic in the accepted momentum range (pT > 0.2 GeV/c);hence, the energy-to-momentum ratio is close to unity.

To further separate electrons and hadrons, we use the TOFinformation from the PbSc part of the EMCal, which covers75% of the acceptance but has a valid time response for 64% ofthe acceptance. In addition, we use the TOF information fromthe TOF-east (TOF-E) detector [36] covering an additional16% of the acceptance. The former has a time resolutionof ∼450 ps, while the latter has a resolution of ∼150 ps.The rest of the acceptance, 9%, does not have a usable TOFcoverage, because the time resolution of ∼700 ps provided byPbGl detectors is not sufficient for an effective separation ofelectrons and hadrons.

D. The hadron-blind detector

The HBD was installed in PHENIX prior to 2010. Adetailed description of the concept, construction, and perfor-mance of the HBD is given in Ref. [27]. Only a brief accountis given here, with emphasis on the specific aspects relevant tothe present analysis.

The HBD provides additional electron identification andadditional hadron rejection to the central-arm detectors. Itsmain task is to recognize and reject γ conversions andπ0 Dalitz decays, which are the dominant sources of thecombinatorial background. Very often, only one of the twotracks of an e+e− pair from these sources is detected in thecentral arm, whereas the second one is lost because it falls outof the acceptance, is curled by the magnetic field, or is notdetected owing to the inability to reconstruct low-momentumtracks with pT < 200 MeV/c. The HBD exploits the fact thatmost of these pairs have a very small opening angle and thusproduce two overlapping hits in the HBD, resulting in a chargeresponse with an amplitude double the one corresponding toa single hit. Being sensitive to electrons down to very lowmomentum (see below), the HBD can detect both tracks andcan effectively reject them by applying a double-hit cut onthe HBD signal. However, decays with a large opening anglebetween the electron and positron produce two well-separatedsingle hits on the HBD pad plane, as illustrated in Fig. 2.The ability to distinguish single from double hits is one of themain performance parameters of the HBD. This is illustrated inFig. 3, which shows the HBD response to single- and double-electron hits in real data. Single and double hits are selected

FIG. 2. Sketch illustrating the HBD response to an e+e− pair fromπ 0 Dalitz decay and from a φ meson decay. The circles represent theCerenkov blobs, whereas the hexagons are the hexagonal pads of theHBD readout plane.

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HBD charge (p.e.)0 20 40 60 80

(arb

. uni

ts)

0

0.1

0.2Single hitsDouble hits

FIG. 3. HBD response to single-electron hits and double electronhits in the 60%–92% centrality bin. The two distributions arenormalized to give an integral yield of one.

from reconstructed low-mass pairs with large (>100 mrad)and small (<50 mrad) opening angles, respectively.

The HBD is a Cerenkov detector. It has a 50-cm-longradiator directly coupled, in a windowless configuration, to atriple gas-electron-multiplier (GEM) detector [37], which has aCsI photocathode evaporated on the top face of the uppermostGEM foil and pad readout at the bottom of the GEM stack(see Fig. 4). The HBD uses pure CF4 at atmospheric pressurethat has an average Cerenkov threshold of γ = 28.8 over thedetector bandwidth, corresponding to a momentum thresholdof ∼15 MeV/c for electrons and ∼4.0 GeV/c for pions.In this scheme, Cerenkov radiation from particles passingthrough the radiator is directly collected on the photocathode,forming a circular blob image rather than a ring, as in a RICHdetector. The pad readout plane comprises hexagonal cellswith a hexagon side of 1.55 cm. One cell subtends an openingangle of approximately 50 mrad and has an area of 6.2 cm2,comparable to the blob size which has a maximum area of10 cm2. The electron response of the HBD is thus typicallydistributed over a maximum of three readout cells and subtendsa maximum opening angle of 75 mrad.

FIG. 4. Triple GEM stack operated in reverse bias mode whereionization electrons produced by a charged particle are repelledtoward the mesh.

The hadron blindness property of the HBD is achievedby operating the detector in reverse bias mode, where themesh defining the detection volume is set at a lower voltagewith respect to the CsI photocathode [25,26] (see Fig. 4).Consequently, the ionization electrons produced by chargedparticles in the drift region defined by the entrance mesh andthe photocathode are mostly repelled towards the mesh. Onlythe ionization electrons created in a thin layer of ∼100 μmabove the photocathode are collected and amplified by theGEM stack, leading to a very small signal, equivalent to a fewp.e., localized in one single cell of the pad plane.

The choice of CF4 in a windowless configuration as thecommon gas for the radiator and the detector amplificationmedium, results in a large bandwidth of UV photon sensitivityfrom 6.2 eV (the threshold of the CsI photocathode) up to11.1 eV (the CF4 cutoff). This translates into an average yieldof 20 photoelectrons (p.e.) per electron, as shown in Fig. 3,corresponding to a measured figure of merit N0 of 330 cm−1,very high for a gas Cerenkov detector [27].

The HBD is located close to the interaction vertex, inthe field-free region, starting immediately after the beampipe at r = 5 cm and extending up to r = 60 cm. Thedetector comprises two identical arms, each covering 112.5◦in azimuth and ±0.45 units of pseudorapidity. The activearea of each arm is subdivided into ten detector modules,five along the azimuthal axis and two along the z axis. Withthis segmentation, each detector module is ∼23 × 27 cm2 insize. The material budget (see Table I) in front of the GEMdetectors is 0.62% of a radiation length dominated by the CF4

contribution of 0.56%. To this one has to add the contributionof the GEM stack, the vessel back plane, and the front-endelectronics attached to the vessel to give a total of 2.4% of aradiation length for the entire detector.

Good gain calibration is crucial to achieve the best possibleseparation between single and double hits in the HBD.Gain variations occur as a function of time owing to twomain factors: (i) variations of temperature and pressure and(ii) charging effects of the GEM foils that produce an initial riseof the gain after switching on the high voltage, which can lastfor several hours before stabilizing [38]. These gain variationsare taken into account by performing a gain calibration ofeach module every 3 min during data collection. This isdone by exploiting the scintillation light produced by chargedparticles traversing the CF4 radiator. The scintillation signalis easily identified by the characteristic exponential shapeof single electrons in the HBD pulse height distribution oflow-multiplicity Au + Au collisions [27]. Furthermore, the

TABLE I. Material budget of the HBD within the central-armacceptance [27].

Component Radiation length(%)

Window (aclar/kapton) 0.04Gas (CF4) 0.56GEM stack 0.42Vessel back plane + front-end electronics 1.4

Total 2.4

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average cell charge per event was found to slowly decreaseby 10%–15% over the 10-week duration of the run for someof the modules. This is attributed to a slow deterioration ofthe quantum efficiency of the photocathodes. This effect wasnoticed in ∼40% of the modules, the others did not show anysign of aging, although all photocathodes were produced underidentical procedures. An additional time-dependent correctionfactor is applied to account for this effect.

In high-multiplicity Au + Au collisions, a large amount ofscintillation light is produced by charged particles traversingthe CF4 gas, resulting in a large detector occupancy. The num-ber of photoelectrons per cell can be as high as ∼10 in the mostcentral collisions. This underlying event background is sub-tracted on an event-by-event basis. For each event and for eachmodule the average charge per unit area 〈Q〉 is calculated as

〈Q〉 =∑

Qcell

/ ∑acell, (1)

where Qcell and acell are the cell charge and area, respectively.The summation is carried out over all the cells of a givenmodule, excluding the cells that are matched to an electrontrack and their first neighbors. The cell charge used for furtheranalysis Q∗

cell is then given by

Q∗cell = Qcell − 〈Q〉 × acell. (2)

After subtraction of the underlying event charge, twoindependent algorithms are used for the HBD hit recognition.The first is a standalone algorithm in which a cluster is formedby a seed cell with Q∗

cell > 3 p.e. together with the fired cells(defined as Q∗

cell > 1 p.e.) among its first six neighbors. Suchclusters can have up to seven cells. A central-arm electrontrack projected onto the HBD readout plane is then matchedto the closest cluster. This algorithm works very well inp + p or peripheral Au + Au collisions, producing a typicalsingle-electron response with an average of 20 p.e. In highermultiplicity events, this algorithm yields a higher charge perelectron and a higher fraction of fake hits as it picks upmore charge from the fluctuations of the underlying eventbackground. Figure 5(a) shows an example of a seed cell andthree of its first neighbors forming a four-cell cluster.

The second algorithm uses the track projection point ontothe HBD to form a cluster around it. The pointing resolution ofa track to HBD is ∼3 mm at pT ∼ 0.5 GeV/c, which is muchsmaller than the size of a pad. The algorithm allows only up

FIG. 5. (a) Standalone cluster formed by a seed cell (red) andthree of its first neighbors resulting in a four-cell cluster. Fired cellsare colored. (b) The same pattern results in a three-cell cluster withthe projection-based algorithm that uses the projection point of anelectron track onto the pad plane.

to three cells in a cluster, depending on the track projectionposition within the cell. If the track projection points to themiddle part of the cell, only that cell is used, but if it pointsto the edge of a cell one or two additional neighboring cellsare summed up in the cluster [39]. The same pattern of firedcells shown in Fig. 5(a) would result in a three-cell cluster inthe projection-based algorithm, as illustrated in Fig. 5(b). Theprojection-based algorithm results in a more precise selectionof the true hit, fewer fake hits, and less pickup of charge fromunderlying event fluctuations.

This is especially important in the most central collisions.However, the limited cluster size truncates the charge informa-tion, resulting in a somewhat reduced efficiency and less powerto discriminate between single and double hits. Therefore, bothalgorithms are utilized in a complementary way, the standaloneproviding a higher efficiency and better single- to double-hitseparation and the projection-based providing a better rejectionof fake hits.

E. Acceptance

1. Acceptance during 2010 run

As mentioned in Sec. II B, the PHENIX central arm magnetswere operated in the +− configuration during the 2010 run.Compared to the standard ++ magnetic field configuration ofPHENIX, the +− configuration has an increased acceptancefor low-pT tracks of about 20%.

Charged particles are bent in the azimuthal direction, φ, bythe magnetic field. Because the DC and RICH are needed toreconstruct the tracks and select the electron candidates, theazimuthal electron acceptance depends on their charge andpT and on the radial location of each detector subsystem. Wedefine the ideal track acceptance of the PHENIX detector inthe +− field configuration by the set of conditions

φmin � φ0 + qkDC

pT

� φmax, (3)

φmin � φ0 + qkRICH

pT

� φmax (4)

θmin � θ0 � θmax, (5)

for tracks originating at z = 0 with charge q, transverse mo-mentum pT , and emission angles φ0 and θ0. kDC = 0.060 rad ×GeV/c and kRICH = 0.118 rad × GeV/c are the effectiveazimuthal bends to the DC and the RICH, respectively. Thepolar angle boundaries of θmin = 1.23 rad and θmax = 1.92 radare defined by the PHENIX central-arm pseudorapidity accep-tance |η| < 0.35. One of the arms covers the azimuthal rangefrom φmin = − 3

16π to φmax = 516π and the other from φmin =

1116π to φmax = 19

16π . The results shown in Sec. V, indicatedas “in the PHENIX acceptance,” refer to the results filteredaccording to this parametrization of the ideal acceptance.

2. Fiducial cuts

Several fiducial cuts are applied to remove inactive areas ofsubsystems or areas with intermittent response to homogenizethe detector response over sizable fractions of the run time.Regarding the operation of the DC, the entire 200-GeV

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Au + Au data set is divided into five groups, with fiducialcuts applied to each group separately such that inside eachgroup the DC has a stable active area. The nonactive DCareas correspond to 19%–31% of the total DC acceptance,depending on the run group.

Fiducial cuts are also applied to the HBD to exclude trackspointing to 1 inactive module of the 20 modules of the HBD.Another fiducial cut removes conversion electrons originatingfrom the HBD support structure, which are strongly localizedin φ near the edges of the acceptance. Other fiducial cuts areapplied to remove inactive or low-efficiency areas in PC1 andEMCal.

In summary, the ideal PHENIX acceptance is reduced bythe fiducial cuts by an amount that varies between 32% and42%, depending on the run group, with an average of 36% forall selected runs.

III. ANALYSIS

This section describes the basic steps of the Au + Audata analysis. It is organized as follows. The data set andevent selection cuts are presented in Sec. III A. Section III Bdescribes the track reconstruction. The methods applied toidentify electrons are presented in detail in Sec. III C and thecuts applied to electron pairs are explained in Sec. III D. Adetailed account of the various background sources and theirsubtraction is provided in Sec. III E. Next we present the rawspectra and corrections (Sec. III F) and discuss the systematicuncertainties (Sec. III G). In the final Sec. III H we discussa second independent analyses used as a cross-check of themain analysis.

A. Data set and event selection

The Au + Au collision data at√

sNN

= 200 GeV werecollected during 2010. Collisions were triggered using theBBCs, with the MB trigger condition (see Sec. II A).

The centrality is determined for each Au + Au collisionfrom the sum of the measured charge in both BBCs combinedwith a Glauber model of the collision [40] as described in Ref.[41]. In this analysis, the data sample is divided into five cen-trality classes: 0%–10%, 10%–20%, 20%–40%, 40%–60%,and 60%–92%. The average number of participants 〈Npart〉 andcollisions 〈Ncoll〉, together with their systematic uncertaintiesassociated with each centrality bin, are summarized in Table II.

TABLE II. Average values of the number of participants 〈Npart〉and number of collisions 〈Ncoll〉 for Au + Au collisions at

√s

NN=

200 GeV with the corresponding uncertainties. The values are derivedfrom a Glauber calculation [40,41].

Centrality (%) 〈Npart 〉 (syst) 〈Ncoll〉 (syst)

0–10 324.0 (5.7) 951.1 (98.6)10–20 231.0 (7.3) 590.1 (61.1)20–40 135.6 (7.0) 282.4 (28.4)40–60 56.0 (5.3) 82.6 (9.3)60–92 12.5 (2.6) 12.1 (3.1)0–92 106.3 (5.0) 251.1 (26.7)

The data were recorded with an online vertex selection ofeither ±20 cm (narrow vertex) or ±30 cm (wide vertex). Theformer selection was applied to the data recorded at the begin-ning of each store, when the luminosity was relatively high.For the latter selection, an additional-offline vertex cut of 30 <z < 25 cm was applied. This asymmetric cut is needed to avoidthe increased yield of conversion electrons originating fromthe side panels of the HBD. These cuts resulted in 1.8 × 109

events with the narrow-vertex selection, 3.8 × 109 events withthe wide-vertex selection, and a total of 5.6 × 109 MB events.

B. Track reconstruction

Charged-particle tracks are reconstructed in the centralarms using the DC and PC1 [32]. The procedure assumesthat all tracks originate from the collision vertex. Eachreconstructed track is then projected onto the other detectors,RICH, EMCal, TOF, and HBD, and the projection points areassociated with reconstructed hits in these detectors.

After a track is reconstructed, the initial momentum vectorof the track at the z vertex is calculated. The transversemomentum pT is determined by measuring the angle αbetween the reconstructed particle trajectory and a line thatconnects the z-vertex point to the particle trajectory at areference radius R = 220 cm. The angle α is approximatelyproportional to charge/pT . In the reverse field configurationused in the 2010 run, the momentum resolution is found to be1.6% at pT = 0.5 GeV/c.

C. Electron identification

1. Detectors and variables used for electron identification

For electron identification, the present analysis uses theHBD along with the central-arm detectors RICH and EMCaland the TOF information from the TOF-E detector and theEMCal. The relevant variables for electron identification fromthese detectors are as follows:

n0, number of hit PMTs in the RICH in the expectedrange of a Cerenkov ring;disp, distance between a track projection and its associ-ated ring center in the RICH;chi2/npe0, a χ2-like shape variable of the RICH ringassociated with the track per npe0, the number ofphotoelectrons measured in the ring;emcsdr, distance between the track projection point ontothe EMCal and the associated EMCal cluster, measured inunits of standard deviation of the momentum-dependentmatching distribution;prob, probability that the EMCal cluster is of electro-magnetic origin, based on the shower shape;dep, variable quantifying the energy-momentum match-ing for electrons. It is defined as dep = E/p−1

σE/p, where

E is the energy measured by the EMCal, p is thetrack momentum, and σE/p is the momentum-dependentstandard deviation of the Gaussian-like E/p distribution;stof(PbSc) and stof(TOF-E), time-of-flight deviationfrom the one expected for electrons measured by eitherthe EMCal-PbSc or the TOF-E detector, converted in

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units of standard deviation of the Gaussian-like TOFdistribution;hbdcharge(P), hbdsize(P), cluster charge and size,respectively, from the HBD projection-based algorithm;hbdid, reduced cluster charge threshold from theprojection-based algorithm. This is the threshold of thehbdcharge(P) variable, which has been tuned to reducethe number of the nongenuine HBD hits by a fixedfactor (e.g., by requiring hbdid � 10, the number of thenongenuine HBD hits is reduced to 1/10 of the initialnumber; these thresholds are tuned depending on eventmultiplicity and HBD cluster size);maxpadcharge(S), charge of the single pad with largestcharge in the cluster of the standalone algorithm;hbdcharge(S), hbdsize(S), cluster charge and size, re-spectively, from the standalone algorithm.

First, electron candidates are selected from the total sampleof tracks that contains mostly hadrons. This is accomplishedby applying very loose cuts such as n0 > 0, which requiresat least one fired PMT around the track projection in theRICH and E/p > 0.4, which rejects the tracks that stronglydeviate from the expected E/p of ∼1. The sample ofelectron candidates selected in such a way comprises thesignal electrons, background electrons (mostly conversionsfrom the HBD back plane), and a relatively large number ofmisidentified hadrons.

2. Exclusion of RICH photomultipliers

The RICH detector in PHENIX uses spherical mirrors toproject the Cerenkov light created by electrons in the radiatorgas onto the PMT plane. As a consequence of this mirrorgeometry, parallel tracks after the field are projected to thesame point in the PMT plane. In other words, if a hadron trackis parallel to an electron track that produces a genuine responsein the RICH, the hadron will appear to have the same responseas the electron and thus it will be misidentified as an electron.Figure 6 shows a typical example of this ring sharing effect. Inthis example, an electron-positron pair is generated by a photonconversion in the HBD backplane. After the magnetic field, ahadron track is parallel to the positron track. Consequently, thehadron and the positron share the same photomultipliers in theRICH detector and the hadron is misidentified as an electron.

This ring-sharing effect occurs because the RICH recon-struction algorithm allows multiple use of fired PMTs bydifferent tracks. The ring sharing is a significant effect. Inthe 2010 run, the majority of electrons are generated by γconversion in the HBD backplane. Although these conversionscan successfully be rejected by the HBD, their response inthe RICH remains and there is some probability that themisidentified hadron will also remain in the pool of electroncandidates.

To reduce PMT sharing by different tracks in the RICH,the original RICH algorithm is modified. The PMTs fired byelectrons that are clearly identified as background electrons,are removed, the ring reconstruction algorithm is reappliedand new n0, npe0, disp, and χ2 variables are derived. Thesebackground electrons are mainly conversion electrons fromthe HBD backplane, electron tracks pointing outside the HBD

FIG. 6. Illustration of a case leading to ring sharing in the RICHdetector. The hadron track parallel to the positron track after themagnetic field will be misidentified as an electron.

acceptance, electrons produced by conversion on the HBDsupport structure, or low-pT electrons with pT < 200 MeV/c.

3. The neural networks

After the initial rejection of nonsignal electrons and thereduction of the ring-sharing effect, the sample of electron can-didates is still highly contaminated by background electronsand misidentified hadrons. A standard procedure to increasethe purity of the electron sample would be to apply a sequenceof one-dimensional cuts on all or some of the 14 variables listedabove. However, such a procedure results in a large efficiencyloss that becomes significant in the e+e− pair analysis wherethe pair efficiency is approximately equal to the single-trackefficiency squared. In this analysis we implement instead amultivariate approach that is based on the neural networkpackage TMultiLayerPerceptron from ROOT [42].

The neural network comprises three layers: the inputlayer, the hidden layer, and the output layer. The input layeris composed of all the input variables normalized to havetheir values between 0 and 1. The hidden layer comprises aselected number of neurons and the output layer comprisesa single output variable. The number of neurons in thehidden layer determines the ability of the neural network todistinguish between the signal and the background, but thisability saturates with increasing number of neurons. For eachneural network, we make sure that the number of neurons issufficiently large to provide the best possible performance,typically 10–15 neurons. In addition, we make sure that asufficient number of tracks is selected for the training sample,such that the performance of the neural network does notdepend on the training statistics. The neural network outputis a single probabilitylike variable, in which values closer to 1mostly correspond to signal, while values closer to 0 mostlycorrespond to background (examples of the neural networkoutput distributions will be shown below). By selecting the

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tracks above a certain threshold, we can reject most of thebackground while keeping a large fraction of the signal.

We use three different neural networks specially trainedon subsets of the large list of eID variables to reject (i)hadrons misidentified as electrons in the central arms (NNh),(ii) background electrons which are mostly HBD backplaneconversions (NNe), and (iii) double hits in the HBD (NNd).In this way we basically have three handles to separatelytreat each type of background. The neural networks learnto distinguish the signal and the background on well-definedsamples. The first two neural networks, NNh and NNe, aretrained on HIJING events. The third neural network NNd istrained on a sample of single-particle event simulations, φ →e+e− decays for single response, and π0 → γ e+e− Dalitzdecays for double response. The training is done separatelyfor each centrality bin to properly treat the multiplicity effects.For centralities >40%, we use the neural network trained forthe 20%–40% centrality bin, where the statistics of the trainingsample is higher. This is justified because already in the20%–40% centrality bin, multiplicity effects are unimportantand the separation between signal and background is good.The training is also done separately for the three cases of TOFinformation (TOF-E, PbSc-TOF, no TOF information).

The simulated events are passed through a GEANT simula-tion of the PHENIX detector and through the same reconstruc-tion code that is used for the data analysis. They are dividedinto two samples. One is used for training purposes and theother one to monitor the neural network output. The simulatedevents are not used to determine absolute efficiencies, whichare determined from simulation, as discussed later in Sec. III F.They are used only for training and monitoring purposes andthe HIJING events are particularly valuable in this respect.They allow us to assess the origin and relative magnitudeof the various background sources at each step of the electronidentification chain, as well as the neural network performancein its ability to reject the background while preservingthe signal. Details of the three neural networks are givenbelow.

4. Hadron rejection

The first neural network, NNh, aims at reducing the hadroncontamination. It exploits the information from all the relevantdetectors, HBD, RICH, EMCal, and TOF-E. The signal (S) forthe training of NNh comprises electron tracks originating at thecollision vertex, whereas the background (B) comprises all theremaining misidentified hadron tracks in the sample.

Figure 7 shows the output values of NNh for the HIJING

monitoring sample (red line) and also shows the output ofNNh applied on real data (black line). The truth informationfrom the HIJING events in terms of signal and background isshown separately. It should be noted that in the HIJING mon-itoring sample, all electron tracks are considered. The signalcomprises the genuine electrons excluding the HBD backplaneconversions and the background is all remaining tracks.

5. Background electron rejection

After rejecting hadrons in the previous step, the dominantbackground in the electron sample comes from the conver-

outputhNN0 0.5 1

Yie

ld

0

1000

2000

3000 Data

HIJING total

HIJING signal

HIJING background

FIG. 7. Comparison of the output values of the neural networkNNh for the 0%–10% centrality bin applied to the HIJING monitoringsample (red line) and to real data (black line). The figure also showsthe signal (green) and the background (blue) components of the HIJING

simulation. The arrow represents the average final cut selected by thecut optimization procedure. See text in Sec. III C 7.

sions in the HBD backplane that were not rejected by theconservative process described in Sec. III C 2. Because theseconversions do not leave a signal in the HBD they can berecognized and rejected if the tracks do not have a matchingHBD response. The rejection capability is, however, limited byfluctuations remaining after the underlying event subtractionin the HBD. To provide the optimal rejection of the remainingbackplane conversions, we use a neural network, NNe, whichis based on the HBD information reconstructed by both thestandalone and the projection-based algorithms. The signaltracks for the training of NNe comprise all signal electronsremaining after the previous step, while the backgroundsample includes only the electrons originating from the HBDbackplane.

Figure 8 shows the distribution of output values of NNe

applied to the HIJING monitoring sample (red line) and to data(black line). The signal and background components of theHIJING simulation are shown separately.

6. Double-hit rejection in the HBD

After removing hadrons and backplane conversions asmuch as possible, the major sources of background are thebeam-pipe and radiator conversions and electrons from π0

Dalitz decays where only one track is reconstructed in thecentral arms. These electrons have a zero or very small openingangle and most of them lead to a double hit in the HBD. Doublehits can be recognized using the HBD response reconstructedin parallel by both the standalone and the projection-basedalgorithms. The response is coupled in a neural network, NNd,separately optimized for different HBD cluster sizes as wellas centrality classes. The NNd cut is an implicit small openingangle cut given by the maximum cluster size which is of theorder of 75 mrad.

Figure 9 shows the distribution of the output variable of theneural network NNd for the separation of single and doublehits in the HBD. The single response is provided by electrons

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outputeNN0 0.5 1

Yie

ld

0

500

1000

1500

2000DataHIJING totalHIJING signalHIJING background

FIG. 8. Comparison of the output values of the neural networkNNe for the 0%–10% centrality bin applied to the HIJING monitoringsample (red line) and to real data (black line). The figure also showsthe signal (green) and the background (blue) components of the HIJING

simulation. The arrow represents the average final cut selected by thecut optimization procedure. See text in Sec. III C 7.

from simulated φ → e+e− decays and the double response byelectrons from π0 → γ e+e− Dalitz decays. The simulationsare embedded into real HBD background events to take intoaccount centrality-dependent occupancy effects.

7. Cut optimization

The final selection of cuts on each neural network outputvariable is optimized using HIJING events. The thresholds arevaried separately to maximize the effective signal, S/

√B.

Because the statistics of the HIJING samples are by farinsufficient for a pair analysis, for the signal S we use thenumber of single electrons from charm decay per event, which

outputdNN0 0.5 1

Yie

ld

0

1000

2000Single hits

Double hits

FIG. 9. The output of the neural network NNd for the recognitionof single and double hits in the HBD. Single response (solid line) isprovided by electrons from simulated φ → e+e− decays and doubleresponse (dashed line) by electrons from π 0 → γ e+e− Dalitz decays.This example is for 30%–40% centrality and for a three-cell clustersize. The arrow represents the average final cut selected by the cutoptimization procedure. See text in Sec. III C 7.

is an easily identified signal in HIJING, and for the backgroundB we use the total number of electrons per event. The cutoptimization is done separately for each centrality class, fortwo pT ranges (pT < 300 MeV/c and pT > 300 MeV/c),for each cluster size, and for each TOF configuration. Theeffective signal for each setup is maximized subject to thefollowing conditions.

(i) The three types of TOF configuration (with PbSctiming information, with TOF-E timing information,and without any timing information), have similarefficiencies with differences of less than 15%.

(ii) Hadron contamination less than 5% for TOF-E andPbSc-TOF and less than 10% for the no-TOF case.

The arrows in Figs. 7–9 represent the average final cutsselected by the cut optimization procedure for these particularcases. The final cuts produce an electron sample with smallhadron contamination, of less than 5%, for all centralities.Strong cuts on the HBD are needed to achieve this smallhadron contamination, resulting in a single-electron efficiencyof 25%–40% depending on centrality, at pT > 0.5 GeV/c (seeSec. III F).

D. Pair cuts

The track selection criteria described above provide anelectron sample with high purity. However, besides thesecriteria which are applied on a track-by-track basis, thisanalysis implements a series of dielectron cuts, based on thepair properties. These cuts are needed to remove ghost pairs,i.e., pairs correlated by the close proximity of tracks in oneof the detectors. Such correlations cannot be described by themixed background, by definition; therefore, this part of thephase space must be removed from both the foreground andthe mixed background. In the present analysis we remove thewhole event, if such a pair is found, as was done in Ref. [23].This procedure removes only ∼2% more of the total pair yieldthan discarding the pairs, because the average pair multiplicityis relatively low.

The most prominent detector correlation comes fromthe ring-sharing effect in the RICH detector, discussed inSec. III C 2, which arises when two tracks are parallel afterthe magnetic field, with at least one of them being an electron.

As mentioned above, the detector-correlated pairs areidentified by applying a cut on the physical proximity of thetracks forming a pair in every detector and the cut value isdetermined by the corresponding double-hit resolution. In theRICH detector, the cut selects pairs whose rings are closerthan 36 cm, which is twice the diameter of the RICH ring(∼16.8 cm). In the EMCal, the cut removes a region of2.5 × 2.5 towers around the hit. In PC1 the pairs are selectedfor removal if their tracks are within 5 cm in z or 0.02 radin φ.

The effect of these three pair cuts on the like-sign andunlike-sign mass spectra is shown in Fig. 10. The like-signyield close to mee ∼ 0 GeV/c2 is affected by all cuts. However,in the unlike-sign foreground spectrum, the cuts affect well-localized regions producing two clearly visible dips. The dipat mee ∼ 0.25 GeV/c2 is created by the RICH pair cut and the

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)2(GeV/ceem0 0.1 0.2 0.3 0.4 0.5 0.6

Yie

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310

Like-sign pairsNo pair cutWith pair cut

(a)

)2(GeV/ceem0 0.1 0.2 0.3 0.4 0.5 0.6

Yie

ld

310

410Unlike-sign pairs

No pair cutWith pair cutDC/PC1 proximity cut

EMCal proximity cut

RICH proximity cut

(b)

FIG. 10. (a) Like-sign and (b) unlike-sign foreground spectrawithout any pair cuts (black) and with RICH, EMCal, and PC1 pairproximity cuts (blue) for MB events.

dip at mee ∼ 0.15 GeV/c2 is created by the PC1 pair cut. TheEMCal pair cut removes yield around 0.20 GeV/c2, but theeffect is small compared to the other two cuts.

In addition to the RICH, EMCal, and DC/PC1 ghost cuts, a100-mrad opening angle cut is applied to remove ghost pairsin the HBD. This is a proximity cut that translates to a distanceof two cells in the pad readout and roughly corresponds to thedouble-hit separation of the HBD. This cut affects the yieldat mee ∼ 0 GeV/c2 in both the like-sign and the unlike-signmass spectra.

E. Background-pair subtraction

Because the origin of the electron track candidates is notknown, all electrons and positrons in the same event are pairedto form the unlike-sign (FG+−) and like-sign (FG++ andFG−−) foreground mass spectra. This gives rise to a largecombinatorial background that increases quadratically withthe event multiplicity. In addition to that, there are severalbackground sources of correlated pairs. The evaluation andsubtraction of the background is the crucial step in the analysisof dileptons in particular in situations, like the present one,where the S/B is at the subpercent level. In this section,we describe in detail the various sources contributing to thebackground and the methodology used to evaluate each ofthem.

1. Background sources

The unlike-sign foreground spectrum FG+− contains, inaddition to the physical signal (S), a large backgroundcomprising the following sources.

(i) Uncorrelated combinatorial background (CB). Thisarises from the random combinations of electrons andpositrons originating from different parent particlesand is an inherent consequence of pairing all electronswith all positrons in the same event. The combinatorialbackground accounts for most of the total background,more than 99% in the most central collisions, andmore than 90% in peripheral collisions. The twoelectron tracks of combinatorial pairs are uncorrelated.However, they carry a global modulation induced bythe collective flow of each individual collision. Theevaluation of the combinatorial background togetherwith the flow modulation is described in detail in thefollowing section (see Sec. III E 2).

(ii) Correlated background pairs. There are three differentsources of correlated background pairs.(a) Cross pairs (CPs). A CP can be produced when

there are two e+e− pairs in the final state of a singlemeson decay. One such case is π0 → e+e−γ →e+e−e+e−. The pair formed by an electron directlyfrom π0 and a positron from γ conversion doesnot come from the same parent particle but it is acorrelated pair through the same primary particle(see Sec. III E 3).

(b) Jet pairs (JPs). The JPs are produced by twoelectrons generated in the same jet or in back-to-back jets (see Sec. III E 4).

(c) Electron-hadron pairs (EHs). Whereas the previ-ous two sources of correlated pairs are of physicsorigin, the EH pairs are an artifact that resultsfrom residual detector correlations that cannot behandled by the pair cuts (see Sec. III E 5).

One can then write

FG+− = S + CB+− + CP+− + JP+− + EH+−. (6)

All the background sources listed above form the yield ofthe like-sign foreground mass spectra FG++ and FG−−. Thereis no signal in these spectra with the exception of a very smallcontribution of e+e+ and e−e− pairs from bb decays (BB). Soone can write

FG++ = CB++ + CP++ + JP++ + EH++ + BB++, (7)

FG−− = CB−− + CP−− + JP−− + EH−− + BB−−. (8)

Usually the like-sign pairs are subtracted from the unlike-sign pairs to obtain the signal. This is a convenient approachin a detector with 2π azimuthal coverage, which ensuresthat the uncorrelated background is charge symmetric, underthe assumption that the correlated background is also chargesymmetric; i.e., it produces the same yield and mass distri-bution of like and unlike pairs. These conditions are not metin the present situation. The two-central-arm configurationof the PHENIX detector results in a substantial acceptance

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difference between like and unlike-sign pairs. Furthermore,the like-sign pairs contain a small signal component frombb decays that needs to be calculated separately. Finally, asshown below, the EH pairs are not charge symmetric. Forthese reasons, in this analysis we adopt a different approachin which each source is evaluated separately for a quantitativeunderstanding of the like-sign yield. Once this is demonstrated,the background sources, CB, CP, JP, and EH are subtractedfrom the inclusive foreground unlike-sign spectrum to obtainthe mass spectrum of the signal pairs. The following sectionsoutline the evaluation of the various background sources.

The BB contribution which is part of the signal is neededonly for the quantitative evaluation of the like-sign spectra.The contribution is calculated using MC@NLO (see Sec. IVfor details), which generates both like-sign and unlike-signcontributions from BB. The small like-sign contribution fromDD is neglected.

2. Combinatorial background

The CB is determined using the event mixing technique, inwhich tracks from different events but with similar character-istics are combined into pairs. In this analysis, all events areclassified into 11 bins in z vertex between −30 and +25 cm,and 10 bins in centrality between 0% and 92%.

In principle, the event-mixing technique is expected toreproduce the shape of the CB with great statistical accuracy,because one can mix as many events as needed to reduce thestatistical uncertainty to a negligible level. In fact, it does notreproduce the shape. There is a small difference between theforeground CB and the mixed-event background. The formeris affected by the elliptic flow, which is intrinsic to heavy-ioncollisions, whereas the latter is obtained by randomly pickingup two tracks from different events and thus on the averagedoes not have any flow effect.

To take into account the effect of flow in the mixedevents, one could make reaction-plane bins, in addition tothe vertex and centrality bins, so that only events with similarreaction plane are mixed. However, the method is limited bythe reaction-plane resolution, and in PHENIX the latter isnot sufficient to reproduce the shape of the foreground CB.Instead, in the present analysis, a weighting method, based onan analytical calculation of the flow modulation, is used toaccount for the flow effects in the mixed events.

If particles are generated according to the distributionfunction

1 + 2v2 cos 2(φ − ψ), (9)

where φ is the particle emission angle in azimuth, ψ is thereaction plane angle, and v2 is the elliptic flow coefficient,then random pairs formed from these particles are distributedas (see Appendix A for the derivation),

P (φa − φb) = 1 + 2v2,av2,b cos 2(φa − φb), (10)

where φa(b) is the azimuthal emission angle and v2,a(b) theelliptic flow of the two particles forming the pair.

In the weighting method, each mixed-background pair isweighted by Eq. (10). The v2 values of inclusive electrons aredetermined from the present data prior to the pair analysis as a

)2 (GeV/ceem0 0.5 1 1.5

For

egro

und/

Bac

kgro

und

0.99

1

1.01

1.02 Simple MixedBG

Weighting methodLike-sign

Simulation

(a)

)2 (GeV/ceem0 0.5 1 1.5

For

egro

und/

Bac

kgro

und

0.99

1

1.01

1.02 Simple MixedBG

Weighting methodUnlike-sign(b)(b)

FIG. 11. Foreground to mixed-background ratio of (a) like-signand (b) unlike-sign mass spectra ratio in a MC simulation. Theforeground is generated with flow, whereas the mixed events areproduced without flow, i.e., using a simple mixed-event technique(squares) and with flow modulation using the weighting method(circles).

function of centrality and electron pT using the reaction-planemethod [43]. Exactly the same cuts as in the data analysis areused in the v2 calculation. The obtained v2 values are in verygood agreement with the inclusive electron v2 values reportedin Ref. [44].

We use a Monte Carlo (MC) simulation to evaluate themethod. The simulation generates electrons and positronsfollowing a Poisson distribution with a mean value of 3.1 Theparticles are uniformly distributed in pseudorapidity between±0.35 and their momentum distribution is taken from data.The azimuthal emission angle φ is determined according tothe distribution 1 + 2v2 cos 2(φ − ψ), where ψ is the reactionplane angle, which is uniformly distributed between ±π

2 . Thev2 values are taken from the 20%–40% centrality bin. Thetracks that pass the PHENIX acceptance filter are used in thepair analysis.

Figure 11 shows the ratio of the foreground to mixed-background mass spectra. The squares correspond to thesimple mixed-event technique without correcting for flow. Wecan see that in this approach the ratio is not flat; i.e., theforeground shape is not reproduced by the mixed-backgroundshape. The circles correspond to the weighting method.The ratio is completely flat over the entire mass range,demonstrating that the weighting method properly accountsfor the flow modulation.

1There is not much meaning to the mean value of 3 of the Poissondistribution. It is a convenient choice to have one pair per event witha high probability.

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A similar MC study was performed to evaluate whethertriangular flow v3 also induces shape distortion of the massspectrum. For the most central collisions, where v3 is compa-rable to v2 at high pT [45], the simulations show that the v3

effect is at least one order of magnitude smaller than for v2

and we thus ignore triangular flow in the determination of theCB shape.

3. Cross pairs

Cross pairs can be produced when a hadron decay producestwo e+e− pairs in the final state. The following hadron decaysand subsequent photon conversions lead to CPs:

π0 → e+1 e−

1 γ → e+1 e−

1 e+2 e−

2 , (11)

π0 → γ1γ2 → e+1 e−

1 e+2 e−

2 , (12)

η → e+1 e−

1 γ → e+1 e−

1 e+2 e−

2 , (13)

η → γ1γ2 → e+1 e−

1 e+2 e−

2 . (14)

The cross combinations give rise to two unlike-sign pairs(e+

1 e−2 and e+

2 e−1 ) as well as two like-sign pairs (e+

1 e+2 and

e−1 e−

2 ) that are not purely combinatorial, but correlated via theπ0 or η mass and momentum. Therefore, this contribution isnot reproduced by the event-mixing technique.

To calculate the CPs, we use EXODUS (see Sec. IV) togenerate π0 and η with the following input parameters:

(i) flat-vertex distribution within |z| < 30 cm (the finalresults are weighted to restore the measured vertexdistribution);

(ii) flat pseudorapidity distribution within |η| < 0.6 anduniform in φ within 0 < φ < 2π ;

(iii) momentum distributions based on PHENIX measure-ments (see Sec. IV).

The generated π0 and η are passed through a GEANT

simulation of the PHENIX detector. By selecting reconstructedCPs, one can determine the shape of the CP invariant massspectrum. The spectra are then absolutely normalized using therapidity density values dNπ0/dy and dNη/dy as a function ofcentrality, summarized in Sec. IV. The absolutely normalizedmass spectra of CPs for the 0%–10% centrality bin are shownin Fig. 12.

4. Jet pairs

The JPs are produced using the PYTHIA 6.319 code withCTEQ5L parton distribution functions [46]. The following hardquantum chromodynamics (QCD) processes are activated[23]:

(i) MSUB 11: fifj → fifj ,(ii) MSUB 12: fif i → fkf k ,

(iii) MSUB 13: fif i → gg,(iv) MSUB 28: fig → fig,(v) MSUB 53: gg → fkf k ,

(vi) MSUB 68: gg → gg,

where g denotes a gluon, fi,j,k are fermions with flavori, j , k, and f i,j,k are the corresponding antiparticles. AGaussian width of 1.5 GeV/c for the primordial kT distribution[MSTP(91) = 1, PARP(91) = 1.5] and 1.0 for the K-factor[MSTP(33) = 1, PARP(31) = 1.0] are used. The minimumparton pT is set to 2 GeV/c [CKIN(3) = 2.0]. The z coordinateof the vertex position is produced uniformly between ±30 cmand then weighted to reproduce the measured distribution.From the PYTHIA output, π0 and η are extracted and passedthrough the GEANT simulator of PHENIX to generate theinclusive e+e− pairs.

In addition to the JPs we are interested in, the foregroundpairs from PYTHIA events contain also “physical” pairs, CPsand combinatorial pairs. The physical pairs and CPs areexcluded from the foreground pairs by requiring that thetwo electrons or positrons of the pair do not share the sameparticle in their history. The CB is statistically subtractedusing the event-mixing technique. The mixed event like-signpairs are normalized to the foreground like-sign pairs in therange �φ

prim0 ∼ π/2, where �φ

prim0 is the difference in the

azimuthal angle of the primary particles, π0 or η. Figure 13shows the �φ

prim0 distributions of the foreground pairs and

the normalized mixed-event pairs. The excess yield around�φ

prim0 ∼ 0 represents the dileptons from the same jet whereas

the excess yield at �φprim0 ∼ π corresponds to the dileptons

from opposite or back-to-back jets.After subtracting the CB, the PYTHIA spectra are scaled to

give the pion yield per p + p MB event. The scaling factoris determined such that the π0 yield in the PYTHIA simulation

)2 (GeV/ceem0 0.2 0.4 0.6 0.8

]-1 )2

[(G

eV/c

evt

Yie

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6−10

5−10

4−100π

η

(a) CP Like-sign: centrality 0-10%

Simulation

)2 (GeV/ceem0 0.2 0.4 0.6 0.8

]-1 )2

[(G

eV/c

evt

Yie

ld/N

6−10

5−10

4−100π

η

(b) CP Unlike-sign: centrality 0-10%

Simulation

FIG. 12. Absolutely normalized (a) like-sign and (b) unlike-sign spectra of cross pairs (CPs) from EXODUS and GEANT simulations for the0%–10% centrality bin. The π 0 and η contributions are shown separately.

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DIELECTRON PRODUCTION IN Au + Au COLLISIONS . . . PHYSICAL REVIEW C 93, 014904 (2016)

(rad)prim

0φΔ

0 1 2 3

)-9

(10

evt

Yie

ld/N

5

10Foreground pairs

Mixed-event pairs

FIG. 13. �φprim0 (difference in the azimuthal angle of the primary

particles, π 0 or η) distributions of foreground and normalizedmixed-event background like-sign pairs as obtained from the PYTHIA

simulations.

matches the measured π0 yield in p + p collisions [47] andfound to be 1/3.9.

The spectra need to be further scaled to obtain the jetcontribution in Au + Au collisions for each centrality bin.This scaling is done following Ref. [48]: A JP originatingfrom primary particles with momenta pT,1 and pT,2 is scaledby the average number of binary collisions 〈Ncoll〉 for eachcentrality bin, times RAA(pT,1), times IAA(pT,2). The same jetor opposite jet IAA(pT,2) values are applied depending on thepair opening angle. The absolutely normalized JP spectra forthe 0%–10% centrality bin are shown in Fig. 14.

5. Electron-hadron pairs

Even after applying the pair cuts described in Sec. III D,EH pairs correlated through detector effects remain in theforeground pairs. An example of such an EH pair can beillustrated with the sketch of Fig. 6 discussed in Sec. III C 2.In this example, if both the positron and the misidentifiedhadron are detected, the pair is identified as a RICH ghost pairand the entire event is rejected by the RICH ghost pair cut asdescribed in Sec. III D. However, if the positron is not detectedowing to detector dead areas or reconstruction inefficiency,the pair formed by the electron and the misidentified hadron

is not rejected and remains in the sample. This pair is nota combinatorial pair but correlated through the positron.Although the misidentification of hadrons via hit sharingoccurs in all detectors, the RICH detector is the dominantcontributor to these EH pairs. Therefore, only the RICHdetector is considered as the source of such correlated pairs.

We simulate EH pairs using electrons from π0 and η simula-tions and hadrons from real events. The π0 and η simulationsare the same ones that are used for the CP simulation. Thehadrons from real events are all the reconstructed tracks thatfail the eID cuts.

The simulation is performed in the following way. First,a combined event is formed using electrons from one Dalitzdecay of π0 or η generated with EXODUS and hadrons froma real event. Second, the information from their associatedfired PMTs is merged and new rings are reconstructed. Usingthe new RICH ring variables, the regular analysis procedure,including eID cuts and pair cuts, is performed on the combinedevent. Finally, the pairs formed by the combination of anelectron track from simulation and a hadron track from dataare extracted. The spectra are absolutely normalized usingthe π0 dN/dy values shown in Sec. IV. The absolutelynormalized EH pair spectra for the 0%–10% centrality binare shown in Fig. 15. Contrary to the CPs and the JPs, wherethe like- and unlike-sign spectra have a very similar shape,the EH pairs exhibit a sizable difference between the like-and unlike-sign spectra. The yield of EH pairs has a strongcentrality dependence. It increases by a factor of ∼50 fromperipheral to central collisions with respect to the π0 rapiditydensity. This increase is mainly attributable to the expectedscaling of the EH pairs with the square of the event multiplicity.

6. Background normalization

The CPs, JPs, EH pairs and BB pairs are absolutelynormalized. The mixed-event technique provides only theshape of the CB. It needs to be normalized to be able tosubtract the background and extract the signal. The only freeparameters of the entire procedure are thus the normalizationfactors of the mixed-event background like-sign spectra nf++and nf−−. They are determined by normalizing the mixed-event background yield (NMIX++(−−) ) to the foreground yield(NFG++(−−) ), integrated over a selected region of phase space,

)2 (GeV/ceem0 1 2 3 4 5

]-1 )2

[(G

eV/c

evt

Yie

ld/N

7−10

6−10

5−10Same jet

Opposite jet

(a) JP Like-sign: centrality 0-10%

Simulation

)2 (GeV/ceem0 1 2 3 4 5

]-1 )2

[(G

eV/c

evt

Yie

ld/N

7−10

6−10

5−10Same jet

Opposite jet

(b) JP Unlike-sign: centrality 0-10%

Simulation

FIG. 14. Absolutely normalized (a) like-sign and (b) unlike-sign spectra of jet pairs (JP) simulated by PYTHIA and GEANT for the 0%–10%centrality bin. The near-side and away-side contributions are shown separately.

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A. ADARE et al. PHYSICAL REVIEW C 93, 014904 (2016)

)2 (GeV/ceem0 0.5 1 1.5 2

]-1 )2

[(G

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evt

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7−10

6−10

5−10

4−10(a) EH Like-sign: centrality 0-10%

Simulation

)2 (GeV/ceem0 0.5 1 1.5 2

]-1 )2

[(G

eV/c

evt

Yie

ld/N

7−10

6−10

5−10

4−10(b) EH Unlike-sign: centrality 0-10%

Simulation

FIG. 15. Absolutely normalized (a) like-sign and (b) unlike-sign spectra of simulated electron-hadron pairs (EH) for the 0%–10% centralitybin. See text for details.

after subtracting the correlated pairs integrated over the sameregion,

nf++ = NFG++ − NCP++ − NJP++ − NEH++ − NBB++

NMIX++,

nf−− = NFG−− − NCP−− − NJP−− − NEH−− − NBB−−

NMIX−−,

where NCP++(−−) , NJP++(−−) , NEH++(−−) , and NBB++(−−) are theintegral yields of each source in the normalization region. Thenormalization region is a window in the azimuthal angulardistance of the two tracks �φ0. It needs to satisfy twocompeting conditions. On the one hand, a small normalizationwindow containing only combinatorial pairs is preferred toavoid being affected by any residual yield (and systematicuncertainties) from the correlated background sources. On theother hand, a wide normalization window is required to reducestatistical uncertainty. The normalization windows used inthis analysis for each centrality bin are shown in Table IIItogether with the corresponding number of like-sign pairs(NLS = NFG++ + NFG−−). The region of small opening anglesthat correspond to small masses where the correlated pairs CP,JP, and EH mostly contribute is excluded in all centrality bins.

The CB in Eqs. (7) and (8) is thus given by the normalizedmixed-event background:

CB++(mee) = nf++ · MIX++(mee), (15)

CB−−(mee) = nf−− · MIX−−(mee). (16)

TABLE III. Normalization window for each centrality bin. Thenumber of like-sign pairs NLS in the window is also shown.

Centrality (%) Normalization window NLS

�φ0

0–10 0.7–3.14 5.1M10–20 0.7–2.1 1.1M20–40 0.7–2.1 660K40–60 0.9–2.1 48K60–92 0.9–2.1 3K

As long as electrons and positrons are produced in pairs andthese pairs are uncorrelated, the total unlike-sign CB yield isthe geometric mean of the total like-sign combinatorial yield,independent of single-electron efficiency and acceptance [23]:

CB+− = 2√

CB++ · CB−−. (17)

A similar relation holds true for the integral yields of themixed-event background:

MIX+− = 2√

MIX++ · MIX−−. (18)

The normalization factor nf+− of the unlike-sign mixed eventbackground is thus deduced from the normalization factors ofthe like-sign mixed background, nf++ and nf−− as

nf+− =√

nf++ · nf−−. (19)

In the present analysis, the square-root relation, Eq. (17), isviolated by two independent factors. First, the relation does nothold true when pair cuts are applied to the spectra because paircuts affect differently the unlike-sign and like-sign spectra.Second, elliptic flow induces an inherent distortion of thesquare-root relation. Flow does not create or destroy particles.It only affects their azimuthal distribution and therefore in aperfect 2π detector there is no effect and Eq. (17) is obeyed.However, in the case of the PHENIX detector, which is nota 2π detector, the relation is violated as demonstrated inAppendix B. Relation (19) can still be used provided thatthe violation is the same in the data and the mixed events. Inthe present analysis, we make sure that this is the case. Westart from a situation in which the mixed events satisfy Eq.(18). We then apply to the mixed events the pair cuts, exactlyas to the foreground events, and the flow modulation using aweighting factor procedure that is based on an exact analyticalcalculation. Thus, we make sure that Eq. (19) is still valid.

7. Quantitative understanding of the background

To illustrate our understanding of the background inquantitative terms, Fig. 16 shows a comparison of the MBmass spectra for the foreground and the calculated backgroundlike-sign pairs.

The top panel shows the foreground like-sign mass spec-trum (open circles) together with the various background

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DIELECTRON PRODUCTION IN Au + Au COLLISIONS . . . PHYSICAL REVIEW C 93, 014904 (2016)

]2 [GeV/ceem1 2

Centrality 0-92%all like-sign pairscombinatorial BGcross pairsjet pairse-h pairs

pairsbb

]2 [GeV/ceem1 2

]-1 )2

[(G

eV/c

evt

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7−10

6−10

5−10

4−10

3−10

2−10Centrality 0-92%

all like-sign pairscombinatorial BGcross pairsjet pairse-h pairs

pairsbb

(a)

)2 (GeV/ceem0 1 2

FG

/All

BG

0.98

1

1.02

(b)

FIG. 16. (a) Measured like-sign spectrum (open circles) togetherwith the calculated background components (histograms) for MBevents. (b) Ratio of the like-sign spectrum to the sum of all thebackground components.

components discussed above (the normalized CB, and theabsolutely calculated CPs, JPs, and EH pairs) and the BB pairscalculated as described in Sec. IV. The bottom panel showsthe ratio of the foreground like-sign spectrum to the sum of allthe background components. Similar comparisons for the fivecentrality bins used in this analysis are shown in Fig. 17.

)2 (GeV/ceem0 1 2

0.81

1.2

Centrality 60-92%(e)

0.95

1

1.05

Centrality 40-60%(d)

0.95

1

1.05

Centrality 20-40%(c)

0.981

1.02

Centrality 10-20%(b)

FG

/All

BG

0.991

1.01

Centrality 0-10%(a)

FIG. 17. Ratios of the like-sign foreground spectrum to the sumof all the background components for the five centrality bins used inthis analysis.

=200 GeV Min. BiasNNsAu+Au

+-FG+-Total BG

Signal

)2 (GeV/ceem0 1 2 3 4 5

S/B

3−10

2−10

1−10

1

]-1 )2

[(G

eV/c

evt

Yie

ld/N

=200 GeV Min. BiasNNsAu+Au

+-FG+-Total BG

Signal

-310

-510

-710(a)

)2 (GeV/ceem0 1 2 3 4 5

S/B

3−10

2−10

1−10

1(b)

FIG. 18. (a) MB mass spectra of the unlike-sign foregroundevents (FG+−), the calculated total background (BG+−) and the rawsignal S. (b) The signal-to-background ratio.

In general, the background is well reproduced in bothshape and magnitude. In particular, for the most centralbins, the background is reproduced with subpercent accuracy.There are, however, a couple of regions where the ratio fore-ground/background is different from one. There is a deviationof the order of a few percent at masses mee < 100 MeV/c2.This is clearly visible in the three most central bins. A numberof factors could be responsible for this deviation, such as scaleerrors in the CPs or the JPs. However, in this mass regionthe signal-to-background ratio is relatively good as shownin Fig. 18 and a deviation of the order of a few percentin the background is negligible. There also seems to be adeviation at mee > 1 GeV/c2 for the 10%–20% and 20%–40%centrality bins. This deviation could indicate underestimationsof the flow or the back-to-back jet contributions, owing tothe precision in these measurements, or the existence of anadditional correlation that is not taken into account in any ofthe calculated background components. To be conservative,this deviation is considered as evidence of unsubtractedbackground and its magnitude is assigned as a mass-dependentsystematic uncertainty of the signal.

Figure 18 shows the MB mass spectra of the foregroundunlike-sign events (FG+−), the calculated total background(BG+−), and the raw signal obtained by their subtraction.The signal to background ratio is shown in the bottom panel.This result is discussed in reference to previously publishedPHENIX results in Sec. V C 1.

F. Raw spectra and efficiency corrections

Figure 19 shows the raw mass spectra, obtained aftersubtracting the pair background, for the five centrality binsof this analysis.

To obtain the invariant mass spectrum inside the idealPHENIX acceptance, the e+e− raw mass yield is corrected

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A. ADARE et al. PHYSICAL REVIEW C 93, 014904 (2016)

)2 (GeV/ceem0 1 2 3 4 5

]-1 )2

[(G

eV/c

evt

Yie

ld/N

11−10

8−10

5−10

2−10

10 = 200GeVNNsAu+Au = 200GeVNNsAu+Au 400×0-10%

20×10-20%20-40%

1/20×40-60% 1/400×60-92%

yield−e+Raw e

FIG. 19. Raw mass spectra for the five centrality bins.

for reconstruction efficiency effects according to

dN

dmee

= 1

Nevt

N (mee)

�mee

1

εtotalpair

, (20)

where Nevt is the number of events, N (mee) is the number ofe+e− pairs with invariant mass mee, and �mee is the massbin width. εtotal

pair is the total pair reconstruction efficiencythat includes the eID efficiency of the neural networks,losses incurred by dead or inactive areas in the detector,pair cut losses, and detector occupancy effects. The total pairreconstruction efficiency εtotal

pair can thus be written as

εtotalpair = εeID

pair · εlivepair · εghost

pair · εmultpair , (21)

where εeIDpair is the e+e− pair reconstruction efficiency including

the efficiency of all the electron identification cuts and the HBDdouble-hit rejection cut, εlive

pair is the pair efficiency from thedetector active area with respect to the ideal PHENIX detectoracceptance, ε

ghostpair reflects the efficiency loss owing to the pair

cuts that remove ghost pairs in the various detectors (seeSec. III D), and εmult

pair is the multiplicity-dependent efficiencyloss discussed below in this section.

The single-electron reconstruction efficiency, defined as ε

=√

εeIDpair · εmult

pair is shown in Fig. 20 vs pT for the five centrality

bins. This efficiency is not actually used in the analysis. It isshown here for illustration purposes. The change of efficiencybelow 0.3 GeV/c arises from the cut optimization in two pT

ranges (see Sec. III C 7).The product εeID

pair · εlivepair · ε

ghostpair is determined as follows. A

cocktail of all the known hadronic sources contributing tothe e+e− pair spectrum is generated within |η| < 0.6 and 2πin azimuthal angle. Details about the various sources of thecocktail are given in Sec. IV. The cocktail is passed through

(GeV/c)Tep

0 0.5 1 1.5 2

ε

0

0.2

0.4

0.6

0.8 Centrality 0-10%

Centrality 10-20%

Centrality 20-40%

Centrality 40-60%

Centrality 60-92%

FIG. 20. Single-electron reconstruction efficiency vs pT for thefive centrality bins.

a full GEANT simulation of the PHENIX detector [49] andanalyzed in the same way as the data, including eID cuts,fiducial cuts, and pair cuts. The resulting output is referred toas the reconstructed cocktail. The ratio of this reconstructedcocktail to the generated cocktail filtered through the idealPHENIX acceptance (but without momentum smearing), givesthe product εeID

pair · εlivepair · ε

ghostpair . This correction is derived in the

two-dimensional space of mass pair pT .Special care is taken to tune the simulations to the data

to ensure that the detector response in the simulations is thesame as in real data for all the subsystems involved in theanalysis. As an example, Fig. 21 shows a comparison of a fewelectron identification variables in data and simulations. Forthis comparison we use a clean sample of electrons providedby fully reconstructed π0 Dalitz decays with an opening anglelarger than 100 mrad from the 60%–92% centrality bin, wherethe occupancy effects are very small and can be ignored. TheeID variables of the two tracks from these pairs are comparedto those of π0 → e+e− γ simulations.

n00 2 4 6 8

(arb

. uni

ts)

0

0.1

0.2

0.3

(a)

dep4− 2− 0 2 4

(arb

. uni

ts)

0

0.05

0.1

0.15

0.2 DataMC(b)

ToF(measured)-ToF(expected) (ns)1− 0 1

(arb

. uni

ts)

0

0.1

0.2

0.3

0.4

(c)

hbdcharge (p.e.)0 50 100

(arb

. uni

ts)

0

0.05

0.1

0.15

0.2 (d)

FIG. 21. Comparison of electron identification variables in data(black) and in simulations (red). The variables are described in Sec.III C. Electrons in data and simulations are from fully reconstructedπ 0 Dalitz decays with opening angle larger than 100 mrad.

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DIELECTRON PRODUCTION IN Au + Au COLLISIONS . . . PHYSICAL REVIEW C 93, 014904 (2016)

TABLE IV. Efficiency loss owing to detector occupancy in thecentral arms εembed

pair and the tagging of RICH PMTs discussed in Sec.III C 2 for the five centrality bins used in this analysis.

Centrality

0%–10% 10%–20% 20%–40% 40%–60% 60%–92%

εembedpair 0.53 0.65 0.76 0.86 0.95

εTPMTpair 0.88 0.92 0.94 0.98 1.00

The HBD occupancy effects are taken into account byembedding the HBD hits from the cocktail simulation intoreal HBD events, and thus are included in the productεeID

pair · εlivepair · ε

ghostpair . There are two other occupancy effects in the

central arms that need to be taken into account and are includedin Eq. (21) by the additional multiplicative factor εmult

pair . Thefirst one is the decrease of track reconstruction efficiency asthe detector occupancy increases with centrality. This lossis referred to as εembed

pair and is determined by an embeddingprocedure. Electrons from φ decays that are reconstructed insingle-particle simulations are embedded into real Au + Auevents. Then the embedded events are run through the fullreconstruction software chain and analyzed in exactly thesame way as the data. The embedding efficiency for singletracks εembed

single is determined as the ratio of the number ofreconstructed electron tracks from embedded data to thenumber of embedded tracks. The pair embedding efficiencyis calculated as the square of the single-track embeddingefficiency, εembed

pair = (εembedsingle )2.

The second occupancy effect comes from the initialrejection of background electrons, discussed in Sec. III C 2,where PMTs fired by background electron tracks are removed.If such an electron is close to a signal electron in the RICH,the associated PMTs of the signal electron are also removed.The probability for this to happen is relatively small andincreases with multiplicity. This loss is referred to as εTPMT

pair

and it is estimated by monitoring the yield of e+e− pairsbelow 20 MeV/c2 before and after erasing the PMTs foreach centrality bin. This mass region is dominated by Dalitzdecays and γ conversions and provides a clean electron pairsample with a signal-to-background ratio of ∼200 even for themost central events. Using these efficiency losses, εmult

pair can beexpressed as

εmultpair = εembed

pair · εTPMTpair . (22)

)2 (GeV/ceem0 1 2 3 4 5

tota

lpa

irε

0

0.1

0.2

Centrality 60-92%

Centrality 40-60%

Centrality 20-40%

Centrality 10-20%

Centrality 0-10%

< 1.0 GeV/cT

0.8 < pair p

FIG. 22. Pair efficiency correction for the pair pT range between0.8 and 1.0 GeV/c for each centrality bin. This represents the totalefficiency including the eID selection cuts based on neural networks,losses in the acceptance owing to detector inactive areas, lossesinduced by the pair cuts, and occupancy effects in the central-armdetectors.

Table IV summarizes the values of εembedpair and εTPMT

pair for thefive centrality bins.

Figure 22 shows the total pair reconstruction efficiency εtotalpair

for pair pT within 0.8–1.0 GeV/c for each centrality bin.

G. Systematic uncertainties

The main systematic uncertainties on the corrected dataarise from uncertainties on the electron identification, the ac-ceptance, and the background subtraction. They are discussedin detail below and summarized in Table V. These uncertaintiesmove all data points in the same direction but not by the samefactor.

1. Systematic uncertainty on electron identification andoccupancy effects

As described in Sec. III C, electron identification is achievedusing three neural networks. Different threshold cuts forthe neural networks result in different electron identificationefficiency and occupancy effects. The thresholds in the neuralnetworks are varied by ±20% around the selected values andthe variations of the electron pair yield in the mass regionmee < 150 MeV/c2, after applying the efficiency correction,are used to assess the systematic uncertainty of electronidentification and occupancy effects.

By changing the thresholds by ±20% the raw electronpair yield changes by about ±50%. However, once the

TABLE V. Summary of systematic uncertainties assigned to the corrected data for MB collisions.

Component Mass range Systematic uncertainty

eID + occupancy effects ±4%Acceptance (time) ±8%Acceptance (MC) ±4%Combinatorial background 0–5 GeV/c2 ±25% (mee = 0.6 GeV/c2)Residual yield 0–0.08 GeV/c2 −5% (mee = 0.08 GeV/c2)Residual yield 1–5 GeV/c2 −15% (mee = 1 GeV/c2)

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A. ADARE et al. PHYSICAL REVIEW C 93, 014904 (2016)

corresponding efficiency corrections are applied, the variationsare below 4% for all the centrality bins. Based on theseresults, we assign a ±4% systematic uncertainty on the electronidentification.

2. Systematic uncertainty on the acceptance

We consider two sources of systematic uncertainties onthe acceptance: variations of the pair acceptance vs timeand variations of the pair acceptance between data and MCsimulations.

The pair acceptance systematic uncertainty vs time isstudied by considering the variations of the number of electronpairs per event for each run group. The weighted average of therms of the number of electrons per event in the five run groupsis found to be 8% and it is taken as the systematic uncertaintyof the acceptance variation over time.

The systematic uncertainty on the data vs MC pair accep-tance is studied by comparing the reconstructed π0 yield indata and simulations. In data we select reconstructed pairs withmee < 100 MeV/c2, after subtracting the combinatorial andcorrelated components of the background, using data from oneof the run groups. In the MC simulations we use reconstructedpairs in the same mass range from π0 Dalitz decays applyingthe fiducial cuts for the corresponding run group. The entiredetector is divided into four sectors. Data and MC simulationsare normalized in one sector. The variations of the yield ratiosbetween data and MC simulations in the other sectors rangesbetween 1% and 8%. The weighted average of these variationsis found to be 4% and it is taken as the systematic uncertainty ofthe acceptance agreement between data and MC simulations.

3. Systematic uncertainty on the background subtraction

We consider two sources of systematic uncertainties on thebackground subtraction.

(i) Uncertainty on the CB subtraction. It is primarilyattributable to the uncertainty in the normalization factor, andthe latter is determined by the statistics in the normalizationwindow, namely by 1/

√NLS (see Sec. III E 6). This translates

into a relative uncertainty of the signal δS/S = 1/√

NLS ×B/S. The ratio B/S depends on both mass and centrality.In Table V we quote the uncertainty at mee = 0.6 GeV/c2,which represents the worst case in mass, for MB events. Thecentrality dependence results in variations of the order of 15%from the MB values.

(ii) In the ideal case, the like-sign residual yield, i.e., thelike-sign yield after subtracting all the background sources,should be zero. In practice it is not. As shown in Figs. 16and 17, there is a small residual yield. In this analysis,we assume that any residual yield is entirely attributable tounsubtracted background, and we take it as an additionalsource of systematic uncertainty, after transforming it intounlike-sign residual yield via the acceptance correction factorα. This uncertainty takes into account any possible discrepancyin shape or magnitude of the various subtracted sources ofbackground. The factor α accounts for the different acceptanceof the PHENIX detector for like- and unlike-sign pairs. It iscalculated as a function of pair mass and pair pT using the

)2(GeV/ceem0 1 2

00.20.40.6 0.03±: 0.065 20-0.08 GeV/c

0.02±: -0.009 21-5 GeV/c

00.05

0.1 0.007±: 0.025 20-0.08 GeV/c0.005±: -0.0011 21-5 GeV/c

0

0.02

0.04 0.002±: 0.013 20-0.08 GeV/c0.0015±: 0.0062 21-5 GeV/c

00.010.02

0.002±: 0.011 20-0.08 GeV/c0.001±: 0.0019 21-5 GeV/c

00.010.02

0.001±: 0.011 20-0.08 GeV/c0.0008±: -0.0012 21-5 GeV/c

)/A

ll B

Glik

eN Δ

α(

(a)

(b)

(c)

(d)

(e)

)2(GeV/ceem0.2 0.4 0.6 0.8

-0.1

0

0.1 60-92%

-0.02

0

0.02 40-60%

-0.0050

0.005 20-40%-0.005

0

0.005 10-20%

-0.002

0

0.002 0-10%

(f)

(g)

(h)

(i)

(j)

FIG. 23. (a)–(e) Unlike-sign residual background yield derivedfrom the like-sign residual yield, obtained after subtracting allbackground sources, via the acceptance correction factor α (see text).The legend and the dashed lines show the results of constant fitsbelow 80 MeV/c2 and above 1 GeV/c2. (f)–(j) Magnified views inthe vertical axis for the 0.2–1 GeV/c2 mass range.

mixed-event background as

α(m,pT ) = MIX+−(m,pT )

MIX++(m,pT ) + MIX−−(m,pT ). (23)

Figures 23(a)–23(e) show α times the like-sign residualyield divided by the sum of all unlike-sign background sourcesas a function of mass for the five centrality bins, whichrepresent the relative residual background yield in the unlike-sign mass spectrum. The mass regions mee < 0.08 GeV/c2,0.2 GeV/c2 < mee < 1.0 GeV/c2 and mee > 1 GeV/c2 arefitted to a constant to quantify the magnitude of the residualunlike-sign yield. The fit results are also shown. Figures23(f)–23(j) show magnified views in the vertical axis forthe 0.2–1 GeV/c2 mass range. The fits in the mass regionmee = 0.2–1.0 GeV/c2 give results that are consistent withzero for all centrality bins. For the other two mass ranges,the residual yields are considered as sources of systematicuncertainties if their significance is larger than 2σ .

The total systematic uncertainty in the background sub-traction is obtained as the quadratic sum of the systematicuncertainties owing to the CB subtraction and the residualyield. Both contributions are listed in Table V for MBcollisions. It is worth noting that the systematic uncertaintyof the background subtraction is much lower than the requiredaccuracy to measure a signal with the S/B values shown inSec. III E 7.

H. Cross checks

A second independent analysis was performed as a cross-check. The key features of the second analysis are discussedhere. A more detailed description is given in Appendix C.

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DIELECTRON PRODUCTION IN Au + Au COLLISIONS . . . PHYSICAL REVIEW C 93, 014904 (2016)

The second analysis is similar to the analysis described inRef. [23], but it makes use of the HBD and includes all theimportant improvements developed in this work. In particular,it makes use of the TOF information for better hadronrejection, implements the shape distortion of the mixed-eventbackground owing to elliptic flow (Sec. III E 2), subtractsthe correlated EH background (Sec. III E 5), and explicitlyconsiders the away-side JP component in the backgroundsubtraction (Sec. III E 4).

Important elements of the independent analysis are differentfrom those of the main analysis. The most significant differ-ences are as follows. (i) The HBD underlying event subtractionis done using the average charge in the vicinity of a track asopposed to the average charge in a module as used in themain analysis. (ii) Electron identification is achieved by asequence of independent one-dimensional cuts on each of theelectron identification variables instead of the neural networkapproach. (iii) The normalization of each background sourceis determined from a fit to the like-sign spectra, in contrast tothe main analysis where all the correlated background sourcesare absolutely normalized and only the CB is normalized tothe like-sign spectra.

The second analysis results in a factor of two smallersignal-to-background ratio and a 10% reduction in purity of theelectron sample in central collisions. However, once correctedfor efficiency, the results of the second analysis are consistentwithin uncertainties with those obtained with the main analysisdescribed in this section.

IV. COCKTAIL OF HADRONIC SOURCES

In this section we describe the procedures used to calculatethe expected dielectron yield from hadronic decays, commonlyreferred to as the hadronic cocktail, which are compared to theexperimental results in Sec. V. The known e+e− sources arecalculated using the EXODUS, PYTHIA, and MC@NLO eventgenerators. EXODUS is a phenomenological generator thatsimulates phase-space distributions of the relevant electronsources and their decays [50]. It generates the photonicsources, i.e., Dalitz decays of light neutral mesons—π0, η, η′→ e+e−γ , and ω → e+e−π0—and the nonphotonic sources,i.e., dielectron decays of mesons: ρ, ω, φ, J/ψ → e+e−.PYTHIA [46] and MC@NLO [51,52] are used to generate thecorrelated pairs from semileptonic decays of heavy-flavor(charm and bottom) mesons. The hadrons are assumed to haveuniform pseudorapidity density within |η| < 0.35 and uniformazimuthal distribution in 2π . Once generated, the sources arefiltered through the ideal acceptance of the PHENIX detectorand smeared with the detector resolution for comparison to themeasured invariant mass spectrum.

A. Neutral pions

The dominant electron source as well as the fundamentalinput for EXODUS is π0. The shape of the π0 pT distribution isparameterized as

Ed3σ

d3p∝ 1(

e−apT −bp2T + pT /p0

)n . (24)

TABLE VI. Fit parameters derived from the π 0 and charged-pionpT distributions [53–55] for different centralities using Eq. (24).

Parameter 0%–10% 10%–20% 20%–40% 40%–60% 60%–92%

a [(GeV/c)−1] 0.57 0.53 0.43 0.36 0.33b [(GeV/c)−2] 0.19 0.16 0.11 0.13 0.088p0 [GeV/c] 0.74 0.75 0.79 0.76 0.74n 8.4 8.3 8.5 8.4 8.4

The parameters, a, b, p0, and n, are obtained by a simultaneousfit of the PHENIX published results for π0 [53,54] and chargedpions [55]. The resulting fit parameters are shown in Table VIfor the five centrality bins of this analysis. The absolutemagnitude of the π0 rapidity density, dNπ0/dy, is obtainedby fitting the cocktail to the data (see Sec. IV D).

B. Other mesons

The pT distributions of other light mesons are basedon the parametrization of the pion spectrum assuming mT

scaling [23]; i.e., Eq. (24) is used with pT replaced by√p2

T + m2meson − m2

π0 . This assumption reproduces well themeasured light meson pT distributions in Au + Au collisionsas demonstrated in Ref. [23]. The absolute normalization foreach meson is provided by the ratio of the meson to π0 invariantyield at high pT (pT � 5 GeV/c). We use the values fromRef. [44], summarized in Table VII.

The values were obtained from p + p collisions and aretaken to be valid for Au + Au collisions because at high pT thesuppression of all mesons is found to be very similar to the π0

suppression and consequently the meson/π0 ratios in Au + Aucollisions remain unchanged with respect to the ratios in p + pcollisions [56–58].

For the pT distribution of the J/ψ we use the neutral pionpT spectrum measured in p + p collisions [47], assumingmT scaling. Detector effects on the J/ψ line shape aretaken into account by passing the decay e+e− through aGEANT simulation of the PHENIX detector. The resulting pT

integrated invariant e+e− mass distribution is then normalizedto the measured cross section in p + p collisions [23] andscaled to Au + Au collisions by the corresponding 〈Ncoll〉 andthe measured RAA for each centrality bin [59].

C. Open heavy flavor

The correlated e+e− yield from open heavy-flavor decays issimulated using two different p + p event generators, PYTHIA

and MC@NLO, and measured cc and bb production crosssections.

TABLE VII. Meson to π 0 ratio at high pT (pT � 5 GeV/c)obtained from PHENIX data in p + p collisions [44].

η/π 0 ρ/π 0 ω/π 0 η′/π 0 φ/π 0

0.48 1.0 0.90 0.25 0.40

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A. ADARE et al. PHYSICAL REVIEW C 93, 014904 (2016)

PYTHIA simulations are used to calculate gluon fusion, thedominant process for heavy-quark production, in leading-orderperturbative QCD. Specifically, we use PYTHIA-6 [60]2 andCTEQ5L as input parton distribution functions. The MC@NLO

package (version 4.03) [51,52] is a next-to-leading-ordersimulation that generates hard scattering events. These eventsare subsequently fed to HERWIG (version 6.520) [61] forfragmentation in vacuum.

We use the cc- and bb-production cross sections measuredby PHENIX [62], by fitting the event generator (PYTHIA orMC@NLO) output to the measured dielectron mass spectrumin d + Au collisions for me+e− > 1.15 GeV/c2. These crosssections were scaled by the average number of d + Au binarycollisions (〈Ncoll〉) to give the p + p equivalent cross section.For bb, both generators gave within uncertainties the sameresult for the cross section extrapolated to zero invariant mass[62]:

dσpp

bb

dy

∣∣∣∣y=0

= 1.36 ± 0.32(stat) ± 0.44(syst) μb. (25)

The cc cross section strongly depends on the eventgenerator. The MC@NLO yields the cross section [62],

dσppcc

dy

∣∣∣∣y=0

= 287 ± 29(stat) ± 100(syst) μb, (26)

whereas PYTHIA gives

dσppcc

dy

∣∣∣∣y=0

= 106 ± 9(stat) ± 33(syst) μb. (27)

This cross section, derived from e+e− data in d + Au colli-sions, is consistent within uncertainties with the cross sectionderived from measurements of single electrons from semilep-tonic decays of heavy-flavor mesons in p + p collisions,extrapolated to pT = 0 GeV/c using PYTHIA simulations [44].MC@NLO was not used to derive the heavy-flavor cross sectionfrom measurements of single electrons.

The two results, Eqs. (26) and (27), although consistentwithin ∼1.2 σ , yield central values which differ by a factorof ∼2.5. This difference comes mainly from the extrapolationof the dilepton yield from mee > 1.15 GeV/c2 to mee = 0GeV/c2, as illustrated in Fig. 24. Figure 24 also shows anabsolute comparison of the PYTHIA and MC@NLO dielectroninvariant yields from correlated heavy-flavor meson decays inMB Au + Au collisions, obtained by Ncoll scaling of the p + pcross sections quoted in Eqs. (26) and (27). At high masses,mee > 1.15 GeV/c2, both generators give by construction thesame yield, with a very small difference in shape. However, atlow masses there is a large discrepancy in the absolute yield.

The d + Au (as well as the p + p) inclusive dilepton yield isnot very sensitive to this variation of the cross section becausethe large effect at low masses is diluted by the contributions

2We use PYTHIA-6 [60] with the following parameters: MSEL[cc] =4 or MSEL[bb] = 5, MSTP(91) = 1, PARP(91) = 1.5, MSTP(33) =1, PARP(31) = 1.0, MSTP(32) = 4, PMAS(4) = 1.25, PMAS(5)= 4.1.

)2 (GeV/ceem0 1 2 3 4 5

]-1 )2

, in

PH

EN

IX a

ccep

tanc

e [(

GeV

/cee

dN/d

m

7−10

6−10

5−10

4−10 =200 GeV Min. BiasNNsAu+Au

ccb)μ/dy = 106 ccσPYTHIA (d

b)μ/dy = 287 ccσMC@NLO (d

FIG. 24. Comparison of the invariant dielectron yield fromcorrelated heavy-flavor meson decays for MB Au + Au collisionscalculated with PYTHIA (solid line) and MC@NLO (dashed line) usingthe dσ

ppcc /dy cross sections of 106 and 287 μb, respectively [62],

scaled by 〈Ncoll〉.

from light meson decays. The situation is quite differentin Au + Au collisions. The yield from light meson decaysscales approximately with Npart, whereas the contribution fromheavy flavor scales with Ncoll, making the latter dominant atlow-masses in central collisions. The choice of the generatorused to simulate the cc contribution will therefore affectthe total cocktail yield at low masses and will influence theinterpretation of the Au + Au data in terms of an excess withrespect to the cocktail. The results are presented in the nextsection using PYTHIA for an easier comparison with previouslypublished results but both generators, PYTHIA and MC@NLO,are considered in the discussion.

D. Cocktail normalization

In the present analysis we use the precisely measured e+e−data at low masses to derive the normalization of the cocktailof hadronic sources. In the restricted phase space defined bymee < 0.1 GeV/c2 and pT /mee > 5 the inclusive e+e− yieldis dominated by π0 Dalitz decays with a small contributionof direct virtual photons and an even smaller contributionof η Dalitz decays. To a very good approximation the massspectrum of these three sources has a 1/mee dependence andtheir relative magnitude is well known. The ratio of directphotons to π0 is known from PHENIX measurements [63,64]and the ratio of η to π0 can be easily obtained from thePHENIX measurement at high pT [58] and the mT scaling asdescribed in Sec. IV B. By fitting the cocktail + direct virtualphotons to the data in the restricted phase space defined above,one obtains the rapidity density dNπ0/dy that determines thenormalization of the cocktail. The values are found to beconsistent with measurements of neutral and charged pions[53–55] within the systematic uncertainties of cocktail anddata.

Alternatively, the cocktail can be absolutely normalizedusing the π0 rapidity density dNπ0/dy derived from thesemeasurements as done in Ref. [23]. The cocktails obtained

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DIELECTRON PRODUCTION IN Au + Au COLLISIONS . . . PHYSICAL REVIEW C 93, 014904 (2016)

)2 (GeV/ceem0 1 2 3 4 5

]-1 )2

, in

PH

EN

IX a

ccep

tanc

e [(

GeV

/cee

dN/d

m

7−10

6−10

5−10

4−10

3−10

2−10 = 200 GeV Minimum BiasNNsAu+Au

Absolute normalization

2<0.1 GeV/ceeNormalization to m

FIG. 25. Cocktail of hadronic sources for the 2010 run withnormalization provided by fitting to the present e+e− invariant yield atmasses mee < 0.1 GeV/c2 (black line) or with absolute normalizationto the π 0 rapidity density derived from measurements of neutral andcharged pions [53–55] (dashed line).

with these two procedures are compared in Fig. 25. The resultsdiffer at masses mee < 100 MeV/c2 by about 25%, which isapproximately the contribution of the virtual direct photons.However, for the mass range of interest, which is typically0.3–0.76 GeV/c2, the difference is smaller and amounts toonly 15%. In this mass range, the yield is dominated bythe contributions from correlated heavy-flavor decays andchanging dNπ0/dy by ∼25% has a minor effect on theinclusive e+e− yield. At even higher masses, mee > 1 GeV/c2,the two procedures yield exactly the same results. Thepresent procedure is adopted to be consistent with the knowncontribution of internal conversion.

E. Systematic uncertainties on the cocktail

The systematic uncertainties of the cocktail ingredientsare estimated and propagated to determine the total cocktailsystematic uncertainty. The following uncertainties are con-sidered.

(i) Light meson to π0 ratio. We adopt the same systematicuncertainties used in Ref. [23], namely ±30% for η, ω, and φ,±33% for ρ, and ±100% for η′.

(ii) Direct photon. The systematic uncertainties in thedirect photon dN/dy are taken from Ref. [64]. They rangefrom ±24% to ±70% from central to peripheral collisions,respectively.

(iii) Open heavy flavor (cc, bb). We use the systematicuncertainties of the open heavy-flavor cross sections given inEqs. (26) or (27) for cc and (25) for bb, taken from Ref. [62].The 〈Ncoll〉 systematic uncertainties shown in Table II areadded in quadrature when the p + p cross sections are scaledto Au + Au collisions.

(iv) J/ψ . The systematic uncertainty of the J/ψ crosssection in p + p collisions is estimated to be ±14% [65]. Thesystematic uncertainties in 〈Ncoll〉 and J/ψRAA are added inquadrature. The RAA uncertainties are taken from Ref. [59],ranging from ±22% to ±35% depending on centrality.

)2 (GeV/ceem0 1 2 3 4 5

Sys

tem

atic

unc

erta

inty

(%

)

50−

0

50

100 Sum*

dirγ

0πη'η

ρωφccbbψJ/

FIG. 26. Systematic uncertainties assigned to each cocktail com-ponent and the total cocktail systematic uncertainty for MB events.

A summary of the cocktail systematic uncertainties ispresented graphically in Fig. 26, which shows the systematicuncertainty of each cocktail component together with the totalcocktail systematic uncertainty, determined as their quadraticsum.

F. The Au + Au cocktail

The cocktail, calculated as described above, using thePYTHIA generator for the open heavy-flavor contributions, ispresented in Fig. 27 for MB Au + Au collisions together withthe individual components of the cocktail. For comparison,Fig. 27 also shows the total cocktail using MC@NLO for theopen heavy-flavor contributions. The differences discussedabove in Sec. IV C are clearly reflected in this comparison.

)2 (GeV/ceem0 1 2 3 4

]-1 )2

, in

PH

EN

IX a

ccep

tanc

e [(

GeV

/cee

dN/d

m

6−10

5−10

4−10

3−10

2−10

= 200 GeV Minimum BiasNNsAu+AuCocktail (PYTHIA)

γ-e+ e→0πγ-e+ e→ηγ-e+ e→'η

-e+ e→ρ0π-e+ e→ω & -e+ e→ω

η-e+ e→φ & -e+ e→φ ee (PYTHIA)→cc ee (PYTHIA)→bb

-e+ e→ψJ/Cocktail (MC@NLO)

FIG. 27. Cocktail of hadronic sources for the 2010 run (blacksolid line) using the PYTHIA generator for the open heavy-flavorcontributions. The individual components of the cocktail are alsoshown. For comparison, the total cocktail using MC@NLO is shown(black dashed line).

014904-23

A. ADARE et al. PHYSICAL REVIEW C 93, 014904 (2016)

FIG. 28. Invariant mass spectrum of e+e− pairs in MB Au + Aucollisions within the PHENIX acceptance compared to the cocktailof expected decays.

V. RESULTS and DISCUSSION

A. Invariant mass spectra

Figure 28 shows the invariant mass spectrum of e+e− pairswithin the PHENIX acceptance (as defined in Sec. II E 1) forMB Au + Au collisions. The spectra are subject to a pT cut of0.2 GeV/c on the single-electron tracks and to a 100-mradcut on the pair opening angle. Statistical and systematicuncertainties on the data points are shown separately byvertical bars and boxes, respectively. Figure 28 also comparesthe measured spectrum to the cocktail of expected e+e−sources, where PYTHIA is used to calculate the correlated pairsfrom heavy-flavor decays. The individual contributions to thecocktail are shown in the figure.

See Sec. IV for details about the cocktail calculation. Thetotal systematic uncertainty of the cocktail is shown by theyellow band. The bottom panel shows the ratio of data tococktail.

Figure 29 shows the invariant mass spectra of e+e− pairsfor the five centrality bins analyzed in this work, compared tothe cocktail.

For a more detailed discussion of the centrality andtransverse momentum dependencies of the dielectron yield,we consider three mass regions:

(a) the mass region mee < 0.10 GeV/c2, which is domi-nated by the π0 Dalitz decay;

(b) the low-mass region (LMR), 0.30 < mee < 0.76GeV/c2, below the ρ meson mass, which is the mostsensitive region to in-medium effects;

(c) the intermediate-mass region (IMR), 1.2 < mee <2.8 GeV/c2, which is dominated by the correlated pairsfrom the semileptonic decays of charm and bottommesons.

)2 (GeV/ceem0 1 2 3 4 5

]-1 )2

, in

PH

EN

IX a

ccep

tanc

e [(

GeV

/cee

dN/d

m-1110

-910

-710

-510

-310

-110

10

3103 10×0-10%

30×10-20%20-40%

1/30×40-60%-3 10×60-92%

= 200 GeVNN

sAu+Au

|<0.35e>0.2 GeV/c, |yeT

p

>0.1radeeΘ

PHENIX

FIG. 29. Invariant mass spectra of e+e− pairs in Au + Aucollisions within the PHENIX acceptance for the various centralitybins. The lines represent the total expected yield from all the sourcesindicated in Fig. 28.

Figure 30 shows the pair pT distribution for these three massintervals in MB collisions. In the following sections we discussthe results in these three mass intervals.

B. π 0 Dalitz region

The mass region mee < 0.10 GeV/c2 is dominated by theπ0 Dalitz decay with a small contribution of direct virtualphotons of ∼20% and an even smaller contribution of the ηDalitz decay of ∼10%. We discuss here only the shape of thepT distribution because the integrated dielectron yield in thismass interval was used to normalize the cocktail for the fivecentrality bins as described in Sec. IV. Figure 30 compares themeasured dielectron pT distribution for MB collisions in thismass interval to the pT distribution of the hadronic cocktail thatuses the parametrization for the π0 and η mesons [Eq. (24)].The agreement between the two distributions, in shape andmagnitude, is very good when adding the measured yield ofdirect virtual photons.

C. Low-mass region

In the LMR, the yield is expected to be saturated by the lightmesons (η,ρ and ω) and the cc contribution. Figure 28 showsan enhancement of e+e− pairs with respect to the cocktailin MB collisions. The enhancement develops with centralityas shown in Fig. 29 and it appears to be distributed over the

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DIELECTRON PRODUCTION IN Au + Au COLLISIONS . . . PHYSICAL REVIEW C 93, 014904 (2016)

FIG. 30. MB-invariant pT distributions for three mass windowsas indicated in the legend. The solid lines represent the expected pT

distributions of the hadronic cocktail and the shadowed bands aroundthe lines represent the cocktail systematic uncertainties. The dottedlines include the contribution from direct photons in the phase-spaceregion where they can reliably be calculated, i.e., pT /mee > 5.

whole pT range covered by the measurement, as can be seenin Fig. 30. We quantify the effect by the enhancement factordefined as the ratio of the measured over expected dileptonyield integrated in the LMR. As discussed in Sec. IV C, thecocktail yield in this mass region depends on the generator,PYTHIA or MC@NLO, used to calculate the open heavy-flavorcontribution. The enhancement factors obtained with PYTHIA

are shown as a function of centrality in Fig. 31 and they arelisted in in Table VIII for the two cases. The enhancementfactors are approximately 40% higher when PYTHIA is usedto calculate the open heavy-flavor contribution instead ofMC@NLO.

1. Comparison to previous PHENIX results

The enhancement factors quoted above are significantlysmaller than those previously reported by PHENIX [23] in thesame Au + Au collision system at the same energy of

√s

NN=

200 GeV. There are a number of significant differences, bothqualitative and quantitative, between the two analyses.

(i) Hadron contamination. The purity of the electronsample is very different in the two cases. In Ref. [23]the hadron contamination was 30% in central Au +Au collisions, whereas in the present analysis, the

partN0 100 200 300

data

/coc

ktai

l

0

2

4

=200 GeVNNsAu+Au 2<0.76 GeV/cee0.3<m

data

cocktail uncertainty

PHENIX

FIG. 31. Data to cocktail (using PYTHIA for heavy-flavor contri-bution) ratio in the LMR versus centrality. The shaded band aroundone represents the cocktail systematic uncertainty.

HBD enabled this contamination to be reduced toless than 5% at all centralities.

(ii) Signal sensitivity. The signal sensitivity is usuallyquantified by the signal-to-background S/B ratio.The S/B values displayed in Fig. 18 are similarto those quoted in Ref. [23]. This is, however, amisleading comparison, because in a situation ofsubpercent S/B ratio, the magnitude of S criticallydepends on the accuracy of the background subtrac-tion. A better way to assess the sensitivity of themeasurement is provided by the cocktail/background,C/B, ratio. From the signal/background ratio andthe enhancement factors quoted in Ref. [23], weestimate an average value of C/B over the massrange mee = 0.15–0.75 GeV/c2 of ∼1/600 in MBcollisions. In the present analysis the same ratio isfound to be ∼1/250. In addition to that, one shouldtake into account that in the 2010 run with the +−field configuration there is a larger track acceptanceof ∼20%. This rough estimate indicates that at thesame multiplicity the signal sensitivity in the presentanalysis is larger by a factor of ∼3.5 compared to theprevious one.

TABLE VIII. Enhancement factors, defined as the ratio ofmeasured over expected dilepton yield in the mass region mee =0.30–0.76 GeV/c2, for the five centrality bins and for MB. Theenhancement factors are quoted separately for the two cases wherethe correlated yield from cc decays is calculated with PYTHIA orMC@NLO. The model uncertainties represent the cocktail systematicuncertainties.

Centrality (%) Enhancement factor ±stat ±syst ±model

MC@NLO cc PYTHIA cc

MB 1.7 ± 0.3 ± 0.3 ± 0.2 2.3 ± 0.4 ± 0.4 ± 0.20–10 2.3 ± 0.7 ± 0.5 ± 0.2 3.2 ± 1.0 ± 0.7 ± 0.210–20 1.3 ± 0.4 ± 0.5 ± 0.2 1.8 ± 0.6 ± 0.7 ± 0.220–40 1.4 ± 0.2 ± 0.3 ± 0.2 1.8 ± 0.3 ± 0.4 ± 0.240–60 1.2 ± 0.2 ± 0.3 ± 0.2 1.6 ± 0.2 ± 0.4 ± 0.260–92 1.0 ± 0.1 ± 0.2 ± 0.2 1.4 ± 0.2 ± 0.3 ± 0.2

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A. ADARE et al. PHYSICAL REVIEW C 93, 014904 (2016)

(iii) Pair cuts. Loose pair cuts were applied in Ref. [23]compared to the cuts used in this analysis. The cutsused in Ref. [23] are found to leave a sizable amount ofdetector-induced correlation in the mass region mee =0.4–0.6 GeV/c2.

(iv) Flow. As demonstrated in Sec. III E 2 the collectiveflow that is inherent to nuclear collisions, affectsthe shape of the combinatorial component of thebackground and violates the square-root relation[Eq. (17)]. These two effects were not taken intoaccount in the data analysis of Ref. [23].

(v) Electron-hadron pairs. As shown in Sec. III E 5, theEH pairs originate in the central-arm detectors andin particular in the RICH detector. This source ofcorrelated pairs was not considered in Ref. [23].

(vi) Away-side jet component. The away-side jet com-ponent of the correlated background was found tobe negligible in Ref. [23] and only the near-side jetcomponent was considered. In the present analysis,both components are absolutely calculated. The away-side component is indeed relatively small but bothcomponents are considered and subtracted.

(vii) Background subtraction procedure. In Ref. [23], theshapes of the three components of the background(CB, CPs, and near-side jet) were calculated, whereastheir absolute scales were obtained by fitting tothe like-sign spectra. In the present analysis, allcomponents of the correlated background (CPs, JPs,and EH pairs) are calculated and subtracted inabsolute terms. There is only one free parameter inthe background subtraction procedure, namely thenormalization factor of the CB.

In conclusion, we do not confirm our previous report ofa large excess seen in the LMR [23]. The differences listedabove affect the yield in the mass region where the excess wasreported but not always in the same direction. For example,the loose pair cuts lead to undersubtraction of the background,whereas neglecting the flow modulation has the oppositeeffect; namely it leads to oversubtraction in the mass regionwhere the excess was observed. These differences also do notaffect the unlike-sign yield by a similar magnitude. The hadroncontamination, the loose pair cuts and the EH pairs are themost significant ones in this respect. Taking all the differencestogether, the present analysis is much improved compared tothe previous one and we thus consider the previous result onthe low-mass excess to be superseded by the results presentedhere.

2. Comparison to STAR results

Recently, STAR published results on e+e− production inAu + Au collisions at

√s

NN= 200 GeV [66,67]. In the same

mass range of mee = 0.30–0.76 GeV/c2, STAR observes anexcess of dielectrons and quotes a value of 1.77 ± 0.11(stat) ±0.24(syst) ± 0.33(model) in MB collisions, for the ratio ofthe dielectron yield to the hadronic cocktail excluding theρ meson contribution. There are two factors that should betaken into account when comparing the STAR results withthose quoted in Table VIII. First, excluding the ρ contribution

partN0 100 200 300

)cda

ta/c

ockt

ail (

PY

TH

IA c

0

1

2

3

4

=200 GeVNNsAu+Au 2<2.8 GeV/cee1.2<m

)cda

ta/c

ockt

ail (

rand

om c

0

2

4

6

datacPYTHIA ccRandom c

PHENIX

FIG. 32. Data to cocktail ratio in the IMR versus centrality. Thecocktail uses PYTHIA for the cc contribution (left scale) or randomcc contribution (right scale). The shaded band represents the PYTHIA

cocktail systematic uncertainty. The same uncertainty applies also tothe random cc cocktail.

results in an increase of about 10% of the data to cocktailratio. Second, STAR uses PYTHIA with a charm cross sectiondσcc/dy = 171 ± 26 μb [66] which is between the PHENIXcross sections quoted in Sec. IV for PYTHIA and MC@NLO.Taking those two differences into account, as well as theexperimental uncertainties, we find that the results of the twoexperiments are consistent in the LMR. The centrality and pT

dependencies of the enhancement reported in Ref. [67] are alsoconsistent with our results.

D. Intermediate-mass region (IMR)

The IMR is dominated by correlated pairs from thesemileptonic decays of DD mesons, with a small contributionfrom BB mesons and an even smaller contribution fromDrell-Yan. The latter is neglected in the cocktail calculation.This mass interval is singled out by theory as the most sensitivewindow to identify the thermal radiation of the QGP in thedilepton spectrum [68,69].

The results displayed in Figs. 28 and 29 show a smallenhancement of dileptons in the IMR with respect to the yieldfrom cc decays calculated using PYTHIA. The enhancementfactors are shown in Fig. 32 as a function of centrality and thevalues are listed in Table IX. The results are consistent withthose of Ref. [23] within the large experimental uncertaintiesof the latter. There is very little difference in the dilepton yieldin this mass interval if MC@NLO is used instead of PYTHIA, asdemonstrated in Fig. 27. The shapes are very similar and theintegral yields in the IMR differ by less than 10% in the twocases.

Using PYTHIA, the enhancement factor in MB events is∼1 standard deviation away from unity. However, the data tococktail comparison discussed above represents an extremecase in which it is assumed that the correlations betweenthe cc pairs in Au + Au collisions are the same as inp + p collisions. It is, however, well known that heavy-flavorquarks exhibit energy loss and collective flow in the mediumformed in Au + Au collisions, as manifested, for example,in measurements of single electrons [44,70]. This shouldaffect the correlation between the e+e− pairs from cc decays.

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DIELECTRON PRODUCTION IN Au + Au COLLISIONS . . . PHYSICAL REVIEW C 93, 014904 (2016)

TABLE IX. Enhancement factors, defined as the ratio of mea-sured to expected dilepton yield in the mass region mee = 1.2–2.8 GeV/c2, calculated using PYTHIA for the five centrality bins andfor MB. The last line gives the enhancement factor assuming randomcorrelation (see text).

Random cc Centrality Enhancement factor ±stat(%) ±syst ±model

PYTHIA cc

0–10 1.3 ± 0.7 ± 0.2 ± 0.310–20 1.8 ± 0.5 ± 0.3 ± 0.320–40 1.8 ± 0.2+0.2

−0.5 ± 0.340–60 1.1 ± 0.2 ± 0.1 ± 0.360–92 1.0 ± 0.2 ± 0.1 ± 0.30–92 1.5 ± 0.3 ± 0.2 ± 0.3

Random cc 0–92 2.5 ± 0.5 ± 0.3 ± 0.3

Lacking a suitable generator to model this effect, we consideralso the opposite extreme approach in which we assumethat the pair is totally decorrelated. The invariant mass iscalculated using two electrons randomly selected from themeasured pT distribution of single electrons from heavy-flavordecays [44], with uniform distributions in pseudorapidity andazimuthal angle. The pair is filtered through the ideal PHENIXacceptance and the integral is normalized to the calculatedPYTHIA yield from cc decays. This extreme case results in asofter mass distribution in the IMR, as can be seen in Fig. 33.

There is a small yield depletion at high masses compensatedby a higher yield at low masses. The integral in the IMR islower resulting in enhancement factors that are ∼70% largercompared to those derived from PYTHIA. The enhancementfactor in MB collisions is quoted in the last line of Table IX

FIG. 33. Invariant mass spectrum of e+e− pairs in MB Au + Aucollisions within the PHENIX acceptance compared to the cocktail ofexpected decays when the cc decay component is calculated assumingno correlation between the c and c.

)2 (GeV/ceem0 0.5 1

]-1 )2

, in

PH

EN

IX a

ccep

tanc

e [(

GeV

/cee

dN/d

m

4−10

3−10

2−10= 200 GeV Min. BiasNNsAu+Au

Sumρcocktail excluding

broadening (Rapp)ρQGP (Rapp)

PHENIX

FIG. 34. MB invariant mass spectrum compared to the modelcalculations of Rapp (solid line) [74]. The main contributions, thein-medium ρ broadening (dotted line), the QGP thermal radiation(dot-dashed line), and the cocktail excluding the ρ (dashed line) arealso shown.

and the centrality dependence is seen by comparing the datapoints to the dot-dashed line in Fig. 32.

E. Comparison to theory

In this section we compare our results to the modeloriginally developed by Rapp and Wambach [71,72]. Themodel uses an effective Lagrangian and a many-body approachto compute the electromagnetic spectral function, which isthe main factor in the calculation of the dilepton productionrates. In the LMR, the spectral function is saturated via vectormeson dominance, by the light vector mesons, in particularthe ρ meson, whereas at larger masses it is dominated bymultipion states or equivalently, via quark-hadron duality,by qq annihilation. The dilepton yields are obtained by anappropriate integration of the thermal rates over the space-timeevolution of the fireball. This model was very successful inreproducing the low-mass dilepton enhancement discovered

(GeV/c)T

p0 1 2 3 4 5

]-1

, in

PH

EN

IX a

ccep

tanc

e [(

GeV

/c)

TdN

/dp 7−10

6−10

5−10

4−10

3−10 = 200 GeV Min. BiasNNsAu+Au

|<0.35e>0.2 GeV/c, |ye

Tp 2<0.76 GeV/cee0.3<m

Sumρcocktail excluding

broadening (Rapp)ρQGP (Rapp)

PHENIX

FIG. 35. Dielectron pT distribution in the LMR compared tomodel calculations (solid line) [74]. The main contributions, thein-medium ρ broadening (dotted line), the QGP thermal radiation(dot-dashed line), and the cocktail excluding the ρ (dashed line) arealso shown.

014904-27

A. ADARE et al. PHYSICAL REVIEW C 93, 014904 (2016)

partN0 100 200 300

in P

HE

NIX

acc

epta

nce

part

Yie

ld/N

0

1

2

6−10×

=200 GeVNNsAu+Au 2<0.76 GeV/cee0.3<m

dielectron excess

broadening + QGP (Rapp)ρ

PHENIX

FIG. 36. Centrality dependence of the dielectron excess, definedas (data − cocktail excluding ρ) compared to the thermal radiationfrom the hadronic (ρ broadening) and QGP phases from modelcalculations (dashed line) [74].

at SPS by the CERES experiment and later further studiedby the NA60 experiment. In the comparison below, we usean improved version of the model that incorporates recentdevelopments, a nonperturbative QGP equation of state andQGP emission rates, i.e., qq annihilation at temperatureshigher than the critical temperature, both based on lattice QCD[73]. It is important to note that this updated version preservesthe agreement with the SPS data and also reproduces the RHICresults from STAR.

Figures 34 and 35 compare the invariant mass spectrumand the LMR pair pT distribution with the model calculationsfor MB collisions [74]. The main components, in-medium ρbroadening, QGP thermal radiation, and cocktail excluding theρ, together with their sum, are shown separately.

In both figures the data are consistent with the calculations.Within this model, the enhancement in the LMR originatesfrom the in-medium ρ broadening, i.e., the thermal radiationof the hadronic phase, with a very small contribution from theQGP.

In the model, the centrality dependence of the thermalradiation is reasonably well described, within an uncertaintyof ∼10%, by a power-law scaling of the charged-particlerapidity density (dNch/dy)α , with α 1.45 [73], very similarto the scaling of the thermal photon yield [64,69]. Withinuncertainties, the present data are consistent with this scalingas illustrated in Fig. 36, which also shows the centralitydependence of the excess, i.e., the data after subtracting thecocktail without the vacuum ρ, together with the expectedpower-law scaling (dashed line).

VI. SUMMARY AND CONCLUSIONS

PHENIX has measured invariant mass spectra, pT dis-tributions, and the centrality dependence of the e+e− pairproduction in Au + Au collisions at

√s

NN= 200 GeV. The

use of the HBD provided additional electron identificationto the central-arm detectors, additional hadron rejection andincreased rejection of the CB.

A new analysis procedure based on neural networkshas been developed that combines in an efficient way theinformation from the HBD and the central arm detectors,RICH, TOF, and EMCal. This results in three independentparameters for electron identification, hadron rejection, andclose pair rejection, instead of the 14 parameters of the fourdetectors involved in these tasks. A quantitative understandingof the total background at the subpercent level is achieved in themost central collisions. This is realized by a precise evaluationof all the background sources. The CB is determined bythe event-mixing technique together with an exact weightingprocedure to take into account the flow effects that are inherentin the foreground events and cannot be reproduced in themixed events. All the correlated background sources arecalculated in absolute terms using simulations and publishedresults.

The results are compared with a cocktail of the knowne+e− sources. The contributions from light hadron decays thatdominate the e+e− yield at low masses mee < 1 GeV/c2, aredetermined using PHENIX measurements for pions and mT

scaling for other mesons. The contributions from semileptonicdecays of heavy-flavor (charm and bottom) mesons arecalculated with the PYTHIA or MC@NLO generators using〈Ncoll〉 scaled p + p cross sections. Both generators givevery similar yields in the IMR. However, they predict verydissimilar results that differ from each other by a factor of∼2 in the LMR. Precise measurements of the charm crosssection over the entire phase space are needed to resolve thisdiscrepancy.

A small enhancement of e+e− is observed in the LMR withrespect to the cocktail. The enhancement is distributed overthe entire pT range measured (pT < 5 GeV/c). It increaseswith centrality and amounts to 2.3 ± 0.4(stat) ± 0.4(syst) ±0.2model for MB collisions when PYTHIA is used to calculatethe open heavy-flavor contribution. If instead MC@NLO isused, the enhancement factors are ∼40% smaller and forMB collisions it is found to be 1.7 ± 0.3(stat) ± 0.3(syst) ±0.2model. The large enhancement of e+e− pairs in the LMRpreviously reported by PHENIX, in Au + Au collisions at√

sNN

= 200 GeV [23], is not confirmed by the results of thepresent improved analysis. In particular, the concentration ofthe excess at low pT (pT < 1 GeV/c) is not observed here. Thepresent results are consistent with those recently published bythe STAR Collaboration [66] within the uncertainties of thetwo experiments.

In the IMR, the results are compared with calculations of theexpected yield from the semileptonic decays of heavy-flavormesons in two extreme scenarios. In the first scenario, theheavy-flavor contribution is calculated assuming that thecorrelations between the cc are the same in Au + Au as inp + p collisions, ignoring decorrelation effects produced bythe interactions of heavy-flavor quarks with the medium. Asmall enhancement is observed with respect to the yield pre-dicted by PYTHIA. It amounts to 1.5 ± 0.3(stat) ± 0.2(syst) ±0.3model for MB collisions. In the other scenario, the oppositeextreme approach is adopted where the pair is assumed tobe totally decorrelated. In this case, the enhancement factorbecomes 2.5 ± 0.5(stat) ± 0.3(syst) ± 0.3model. The reality issomewhere between these two extreme cases and we conclude

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DIELECTRON PRODUCTION IN Au + Au COLLISIONS . . . PHYSICAL REVIEW C 93, 014904 (2016)

that there is room in the data for a significant additionalcontribution, for example, of thermal radiation, in the IMR.The nature of the IMR pairs will be studied with high-statisticsAu + Au data in 2014 data taking with the silicon vertextracker (VTX) installed in PHENIX.

The results in the LMR are compared to calculations basedon the model originally developed by Rapp and Wambach[71,72] with subsequent improvements that incorporate recentdevelopments [73]. The model includes thermal radiationemission from the QGP phase (qq annihilation), as well asfrom the hadronic phase (mainly from the ρ meson copiouslyproduced by pion annihilation, π+π− → ρ → e+e−). Theinvariant mass and pT distributions, as well as the centralitydependence, are well reproduced by the calculations. Theenhancement observed in the LMR from SPS up to RHICenergies is thus consistently reproduced by a single model.Within this model, the enhancement originates from themelting of the ρ meson resonance as the system approacheschiral symmetry restoration.

ACKNOWLEDGMENTS

We thank the staff of the Collider-Accelerator and PhysicsDepartments at Brookhaven National Laboratory and the staffof the other PHENIX participating institutions for their vitalcontributions. We also thank R. Rapp for providing us theresults of his model calculations and for helpful discussions.We acknowledge support from the Office of Nuclear Physicsin the Office of Science of the Department of Energy, theNational Science Foundation, Abilene Christian UniversityResearch Council, Research Foundation of SUNY, and Deanof the College of Arts and Sciences, Vanderbilt University(USA); Ministry of Education, Culture, Sports, Science, andTechnology and the Japan Society for the Promotion of Science(Japan); Conselho Nacional de Desenvolvimento Cientıficoe Tecnologico and Fundacao de Amparo a Pesquisa doEstado de Sao Paulo (Brazil); Natural Science Foundationof China (People’s Republic of China); Croatian ScienceFoundation and Ministry of Science, Education, and Sports(Croatia); Ministry of Education, Youth and Sports (CzechRepublic); Centre National de la Recherche Scientifique,Commissariat a l’Energie Atomique, and Institut National dePhysique Nucleaire et de Physique des Particules (France),Bundesministerium fur Bildung und Forschung, DeutscherAkademischer Austausch Dienst, and Alexander von Hum-boldt Stiftung (Germany); National Science Fund, OTKA,Karoly Robert University College, and the Ch. Simonyi Fund(Hungary); Department of Atomic Energy and Department ofScience and Technology (India); Israel Science Foundation(Israel), Basic Science Research Program through NRF of theMinistry of Education (Korea); Physics Department, LahoreUniversity of Management Sciences (Pakistan); Ministry ofEducation and Science, Russian Academy of Sciences, FederalAgency of Atomic Energy (Russia); VR and WallenbergFoundation (Sweden); the U.S. Civilian Research and De-velopment Foundation for the Independent States of theFormer Soviet Union, the Hungarian American EnterpriseScholarship Fund, and the US-Israel Binational ScienceFoundation.

APPENDIX A: INTRODUCING FLOW IN THE MIXEDEVENTS

In this section, we analytically derive the weighting factorintroduced in Eq. (10). We start from the azimuthal distributionof a particle that follows the expression

P (φ − �) = ε(φ)[1 + 2v2 cos 2(φ − �)], (A1)

where φ is the azimuthal angle of the particle, � is the reactionplane azimuthal angle of the event, and ε(φ) is the detectionefficiency of the spectrometer at φ.

The �φ distribution of any two particles in the same event(foreground pairs) can be calculated as

PFG(�φ)

= 1

π

∫ π/2

−π/2d�

∫φ1−φ2=�φ

dφ1dφ2P (φ1 − �)P (φ2 − �)

= 1

π

∫ π/2

−π/2d�

∫ π

−π

dφ1P (φ1 − �)P (φ1 + �φ − �). (A2)

Replacing P (φ − �) with its expression in (A1) allows oneto write PFG as the sum of four integrals,

PFG(�φ) = 1

π

∫ π/2

−π/2d�

∫ π

−π

dφ1(A + B + C + D), (A3)

A = ε(φ1)ε(φ1 + �φ), (A4)

B = 2v2ε(φ1)ε(φ1 + �φ) cos 2(φ1 − �), (A5)

C = 2v2ε(φ1)ε(φ1 + �φ) cos 2(φ1 + �φ − �), (A6)

D = 4v2v2ε(φ1)ε(φ1 + �φ)[cos 2(φ1 − �)]

× [cos 2(φ1 + �φ − �)]. (A7)

It is easy to show that the integrals of B and C are equal to0 and the integral of D leads to

1

π

∫ π/2

−π/2d�

∫ π

−π

dφ1D

= 2v2v2 cos 2�φ

∫ π

−π

ε(φ1)ε(φ1 + �φ). (A8)

Therefore,

PFG(�φ) =[∫ π

−π

dφ1ε(φ1)ε(φ1 + �φ)

]

×(1 + 2v2v2 cos 2�φ). (A9)

In a similar way one can calculate the �φ distribution ofmixed BG pairs produced without reaction-plane binning,

PMIX(�φ)

= 1

π2

∫ π/2

−π/2d�1

∫ π/2

−π/2d�2

∫φ1−φ2+�φ

×dφ1dφ2P (φ1 − �1)P (φ2 − �2), (A10)

where φ1(2) and �1(2) represents the azimuthal angle of particle1(2) and the reaction-plane azimuthal angle of the eventsfrom which the particles are taken. Replacing P (φ − �)

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A. ADARE et al. PHYSICAL REVIEW C 93, 014904 (2016)

with (A1),

PMIX(�φ) = 1

π2

∫ π/2

−π/2d�1

∫ π/2

−π/2d�2

∫φ1−φ2+�φ

×dφ1dφ2(E + F + G + H ), (A11)

E = ε(φ1)ε(φ1 + �φ), (A12)

F = 2v2ε(φ1)ε(φ1 + �φ) cos 2(φ1 − �1), (A13)

G = 2v2ε(φ1)ε(φ1 + �φ) cos 2(φ1 + �φ − �2),

(A14)

H = 4v2v2ε(φ1)ε(φ1 + �φ) cos 2(φ1 − �1)

× cos 2(φ1 + �φ − �2). (A15)

Because F , G, and H are again easily proved to be 0,PMIX(�φ) can now be written as

PMIX(�φ) =∫ π

−π

dφ1ε(φ1)ε(φ1 + �φ). (A16)

The weighting factor to introduce the flow correlation intothe mixed BG pairs is then given by the ratio between Eq. (A10)and Eq. (A16):

w(�φ) = PFG(�φ)

PMIX(�φ)= 1 + 2v2v2 cos 2�φ. (A17)

APPENDIX B: VIOLATION OF CB+− = 2√

CB++CB−−OWING TO FLOW

In this appendix, we demonstrate that the combinationof elliptic flow and nonuniform detection efficiency violatesthe well-known relation between unlike-sign and like-signCB:

〈CB+−〉 = 2√

〈CB++〉〈CB−−〉 (B1)

where 〈CB+−/++/−−〉 are the unlike-sign and like-sign integralyields or average numbers of pairs per event.

We start from the case without elliptic flow. Then, asproven in Ref. [23], if e+ and e− are always producedin pairs independent of each other, the average number ofunlike-sign and like-sign combinatorial pairs can be calculatedas

〈CB+−〉 = [εp + ε+(1 − εp)][εp + ε−(1 − εp)]

×(〈N2〉 − 〈N〉), (B2)

〈CB++〉 = 12 [εp + ε+(1 − εp)]2(〈N2〉 − 〈N〉), (B3)

〈CB−−〉 = 12 [εp + ε−(1 − εp)]2(〈N2〉 − 〈N〉), (B4)

where εp is the probability to reconstruct both tracks of a pair,ε+/− is the probability to reconstruct only a single track, andN is the number of pairs in an event.

If εp/+/− are assumed to be constants, Eq. (B1) can easilybe proven from Eqs. (B2)–(B4). However, in the presence ofelliptic flow, the probabilities εp/+/− depend on the reaction

plane angle:

εp/+/−(ψ) =∫

dφ εp/+/−(φ)[1 + 2v2 cos(φ − ψ)], (B5)

〈CB+−(ψ)〉 = [A(ψ)B(ψ)] × (〈N2〉 − 〈N〉), (B6)

〈CB++(ψ)〉 = 12 [A(ψ)]2 × (〈N2〉 − 〈N〉), (B7)

〈CB−−(ψ)〉 = 12 [B(ψ)]2 × (〈N2〉 − 〈N〉), (B8)

A(ψ) = εp(ψ) + ε+(ψ)[1 − εp(ψ)], (B9)

B(ψ) = εp(ψ) + ε−(ψ)[1 − εp(ψ)]. (B10)

Taking the average over ψ within [−π2 , π

2 ] gives

〈CB+−〉 = (〈N2〉 − 〈N〉)∫

dψA(ψ)B(ψ), (B11)

〈CB++〉 = 12 (〈N2〉 − 〈N〉)

∫dψA(ψ)2, (B12)

〈CB−−〉 = 12 (〈N2〉 − 〈N〉)

∫dψB(ψ)2. (B13)

Using the Cauchy-Schwarz inequality, one obtains[∫

dψA(ψ)B(ψ)

]2

�∫

dψA(ψ)2∫

dψB(ψ)2 (B14)

and, consequently,

〈CB+−〉 � 2√

〈CB++〉〈CB−−〉. (B15)

APPENDIX C: A SECOND, INDEPENDENTANALYSIS

A subset of the data, 4.8 × 109 MB events, was analyzedby a second independent team. The second analysis followsthe analysis strategy presented in Ref. [23], but includesthe information provided by the HBD and other importantimprovements developed in this work.

In this appendix we present the key features of the secondanalysis with an emphasis on the most important differencesto the main analysis: (i) the HBD underlying event subtractionand cluster algorithm, (ii) the electron identification cuts,and (iii) the background normalization. All analysis steps notexplicitly mentioned are identical between the two analyses.In particular, identical cuts on the acceptance and inactivedetector areas, and the same pair cuts are applied. At the end ofthis appendix we discuss the efficiency correction and comparethe results of both analyses.

The net number of photo electrons in an HBD clusterwas calculated with a different algorithm than discussedin Sec. II D, using a local estimate of the scintillationbackground rather than a module average. As an electrontypically fires three HBD readout cells, three-cell triplets areused to initiate the cluster search. All possible triplets areformed. The photoelectron background owing to scintillationlight is estimated by the median amplitude in the first andsecond neighboring cells around the triplet. The background-subtracted triplet charge is calculated as

qnet = qt − At × 〈qfn〉 + 〈qsn〉2

, (C1)

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where qt is the total charge in the triplet, At the number ofcells with charge in the triplet, and 〈qfn〉, 〈qsn〉 are the mediancharge in the first and second neighboring cells, respectively.Only triplets with 0 < qnet < 60 p.e. are recorded.

Electron candidates are projected to the HBD, and tripletswithin 1.5 cm of the track are merged to form a cluster. Thenet charge of the cluster qr is calculated starting from the sumof the charge of all cells in the cluster,

qr = qtotclust − Aclust × 〈qfn〉 + 〈qsn〉2

, (C2)

where qtotclust is the sum of the charge of all cells in the cluster,Aclust is the number of cells in the cluster, and 〈qfn〉, 〈qsn〉are again the median charge per cell in the first and secondneighbors but now around the cluster.

This analysis uses a number of sequential one-dimensionalcuts to identify electrons. The variables used for the electronidentification are defined in Sec. III C 1. The following cutsare used:

(i) n0 > 2, the exclusion of RICH photomultipliers firedby background electrons (Sec. III C 2) is not used inthis analysis;

(ii) disp < 5.5 cm;(iii) chi2/npe0 < 20;(iv) emcsdr < 3;(v) |dep| < 2;

(vi) m2TOF < 1.5σ , calculated based on the TOF measured

by either the EMCal or the TOF-E detectors;(vii) 10 < qr < 40 p.e., cluster charge as defined in

Eq. (C2).

With these cuts, a purity of the electron sample of 86% isachieved for the most central bin, which quickly increases toabove 99% for the most peripheral collisions.

The CB is calculated by event mixing. We use the methodoutlined in Ref. [23], but included the weighting for theazimuthal anisotropy as implemented in the main analysis anddescribed in Sec. III E 2. For the correlated background bothanalyses use the same MC simulations. For CPs and JPs thesimulated pairs were reanalyzed with the track selection cutsand HBD cluster algorithm mentioned above. The shapes ofthe mass spectra are consistent within systematic uncertaintiesfor the two analysis methods. For the EH and BB contributionsthe simulated pairs were not reanalyzed.

The normalizations of all the background components werefitted simultaneously to the full mass and pT range of thelike-sign spectra:

FG++−− = a0BG++−− + a1CP++−− + a2JPsame++−−

+ a3JPopposite++−− + a4EH++−− + a5BB++−−.

(C3)

The parameters ai are the individual normalization constants.Figure 37 shows the like-sign foreground divided by the sumof all background sources for the five centrality classes. Theuncertainty on the CB normalization is shown as a grayband on each panel. No systematic deviation from unity isobserved, indicating that the sum of the different backgroundcomponents gives a sufficiently accurate description over the

FG

/All

BG

0.9951

1.0051.01 (a) 0-10%

0.9951

1.0051.01 (b) 10-20%

0.9951

1.0051.01 (c) 20-40%

0.981

1.02 (d) 40-60%

)2 (GeV/ceem0 0.5 1 1.5 2

0.951

1.051.1 (e) 60-92%

FIG. 37. The ratio of the foreground like-sign pairs to the sum ofcombinatorial and correlated pair sources in centrality bins 0%–10%,10%–20%, 20%–40%, 40%–60%, and 60%–92%.

mass range up to 2 GeV/c2 with no indication of any shapevariation within the shown uncertainties. Above 2 GeV/c2 thestatistical significance makes a comparison at the shown scalemeaningless.

After fixing the normalization of all background sourcesso that a satisfactory description of the like-sign pairs isachieved, the analysis is extended to unlike-sign pairs. Thenormalizations for the unlike-sign CPs, JPs, and EH pairs aretaken from Eq. (C4). For the combinatorial unlike-sign pairswe use unlike-sign mixed-event pairs. The normalization isalso taken from Eq. (C4), but needs to be corrected to accountfor the different effect of the pair cuts on like- and unlike-signpairs as done in Ref. [23].

To estimate the uncertainty on the raw yield owing to thebackground subtraction, one needs to consider the signal-to-background ratio S/B. The uncertainties on the ai aremultiplied by B/S and added in quadrature. This resultsin ∼55% systematic uncertainties at 0.6 GeV/c2 for MBcollisions.

We factorize the efficiency into three terms, which aredetermined separately:

εtotalpair = εpair · εTOF

pair · εembedpair . (C4)

The first factor describes the effect of all reconstructionalgorithms and cuts except for the TOF cut and the centralitydependence of the reconstruction efficiency in the centralarms, which are treated separately. It is obtained by a MCsimulation of e+e− pairs that are processed through thefull PHENIX detector simulation, including the HBD. Thesimulated HBD hits are embedded into real HBD data asdiscussed in Sec. III F. These events are then analyzed withthe same electron identification, fiducial, and pair cuts used in

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A. ADARE et al. PHYSICAL REVIEW C 93, 014904 (2016)

)2(GeV/ceem0 1 2 3 4

]-1 )2

in P

HE

NIX

acc

epta

nce

[(G

eV/c

eedN

/dm

11−10

9−10

7−10

5−10

3−10

1−10

10

310M 3 10×S 0-10% M 30×S 10-20% M S 20-40%M 1/30×S 40-60% M -3 10×S 60-92%

Au+Au

=200GeVNNs

FIG. 38. Comparison of final spectra from the main (M) andsecond (S) analyses.

the independent analysis, with exception of the TOF cut. Thesystematic uncertainty of εpair is about 12%. It was determined

from the measured yield of pairs in the π0 Dalitz decay regionwhen varying electron identification cuts in a way that changesthe raw pair yields by factors between 0.5 and 1.5.

The efficiency εTOFpair is determined from tracks measured

in peripheral collisions, where the hadron contamination isnegligible, by comparing data obtained with a 1.5σ cut tothe case with no TOF cut. We find that on average the TOFefficiency for tracks is 93% above 0.4 GeV/c, but drops to80% at 0.2 GeV/c independent of centrality. This drop resultsfrom a failure of the electronics to properly record time forlow-amplitude signals. In the main analysis this issue wasavoided by treating tracks with no time information separately.The systematic uncertainty owing to this cut is a few percentat 0.6 GeV/c2.

The efficiency εembedpair was determined by embedding MC-

simulation tracks into the data of all used central-arm detectorsand analyzing these embedded tracks using the same cuts asused in the data. The values are found to be very similar tothose derived in the main analysis. For central collisions, anadditional 8% systematic uncertainty is added.

Compared to the main analysis, the total reconstructionefficiency εtotal

pair is a factor of ∼2 smaller for central collisions.The difference drops to ∼30% for the most peripheralcollisions.

The fully corrected mass spectra from the independentanalysis are compared to those from the main analysis inFig. 38 for all five centrality bins. The results are consistentwithin uncertainties.

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